Boris Guljas - Academia.edu (original) (raw)
Papers by Boris Guljas
Real Analysis Exchange, 1996
We analyse an algorithm of transition between Cauchy problems for secondorder wave equations and ... more We analyse an algorithm of transition between Cauchy problems for secondorder wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the standard conditions guaranteeing well-posedness. The typical operations involved in rewriting equations into systems are then neither defined classically nor consistently extendible to the distribution theoretic setting. However, employing the nonlinear theory of generalized functions in the sense of Colombeau we arrive at clear statements about the transfer of questions concerning solvability and uniqueness from wave equations to symmetric hyperbolic systems and vice versa. Finally, we illustrate how this transfer method allows to draw new conclusions on unique solvability of the Cauchy problem for wave equations with non-smooth coefficients.
Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators ... more Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators on W are reduced by a suitable Hilbert space contained in W. This enables us to describe bounded E-linear operators by lifting the appropriate results from Hilbert space theory. In particular, generalized compact E-linear operators are characterized.
Journal of Operator Theory, 2008
Revue Roumaine des Mathematiques Pures et Appliquees
Proceedings of the American Mathematical Society
Let W be a Hilbert C*-module over the C*-algebra A ≠ C of all compact operators on a Hilbert spac... more Let W be a Hilbert C*-module over the C*-algebra A ≠ C of all compact operators on a Hilbert space. It is proved that any function T: W → W which preserves the absolute value of the A-valued inner product is of the form Tv = φ(v)Uv, v ∈ W, where φ is a phase function and U is an A-linear isometry. The result generalizes Molnár's extension of Wigner's classical unitary-antiunitary theorem.
Acta Scientiarum Mathematicarum
A theorem of P. A. Fillmore and J. P. Williams [Adv. Math. 7, 254-281 (1971; Zbl 0224.47009)] imp... more A theorem of P. A. Fillmore and J. P. Williams [Adv. Math. 7, 254-281 (1971; Zbl 0224.47009)] implies that a bounded operator A on a separable Hilbert space H is compact if and only if it satisfies lim n Ae n =0, or equivalently, lim n (Ae n |e n )=0 for each orthonormal basis (e n ) for H. In the present note this theorem is reproved using the fact observed by Halmos that each sequence of unit vectors weakly converging to 0 approximately contains an orthonormal subsequence. It is also noted that the stronger version of the theorem remains true, namely without the continuity assumption on A. In the second part of the note the bounded operators for which there exists an orthonormal basis such that either of the above equalities holds are exhibited and completely described.
Journal of Computational Analysis and Applications - J COMPUT ANAL APPL, 2001
We establish a result which subsumes two versions of the extended reversed Meir inequality.
Journal of Mathematical Physics, 2003
Let H be a complex Hilbert space, dim H > 1, and let A ⊆ B(H) be a C *-algebra such that the idea... more Let H be a complex Hilbert space, dim H > 1, and let A ⊆ B(H) be a C *-algebra such that the ideal K(H) of all compact operators on H is contained in A. Let X be a Hilbert C *-module over A. We prove that any function F : X → X which preserves the absolute value of the A-valued inner product on X is of the form F (x) = ϕ(x)U x, x ∈ X, where ϕ is a phase function and U is an A-linear isometry. The result generalizes Wigner's classical unitary-antiunitary theorem and its extension to Hilbert K(H)-modules.
Glasnik Matematicki, 2003
We describe the pullback construction in the category of Hilbert C *-modules (with a suitable cla... more We describe the pullback construction in the category of Hilbert C *-modules (with a suitable class of morphisms) in terms of pullbacks of underlying C *-algebras. In the second section the Busby invariant for extensions of Hilbert C *-modules is introduced and it is proved that each extension is uniquely determined, up to isomorphism, by the corresponding Busby map. The induced extensions of the underlying C *algebras as well as of the corresponding linking algebras are also discussed. The paper ends with a Hilbert C *-module version of a familiar result which states that a C *-algebra is projective if and only if it is corona projective. 2000 Mathematics Subject Classification. 46C50, 46L08. Key words and phrases. Hilbert C *-module, adjointable operator, extension, multiplier algebra.
Journal of Operator Theory, 2001
Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators ... more Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators on W are reduced by a suitable Hilbert space contained in W. This enables us to describe bounded E-linear operators by lifting the appropriate results from Hilbert space theory. In particular, generalized compact E-linear operators are characterized.
The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1998
An integral inequality is established involving a probability density function on the real line a... more An integral inequality is established involving a probability density function on the real line and its first two derivatives. This generalizes an earlier result of Sato and Watari. If f denotes the probability density function concerned, the inequality we prove is thatunder the conditions β > α 1 and 1/(β+1) < γ ≤ 1.
The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1998
A new version of Jensen's inequality is established for probability distributions on the nonnegat... more A new version of Jensen's inequality is established for probability distributions on the nonnegative real numbers which are characterized by moments higher than the first. We deduce some new sharp bounds for Laplace-Stieltjes transforms of such distribution functions.
To evaluate the physico-chemical and hydrological characteristics of cocopith, perlite, vermicull... more To evaluate the physico-chemical and hydrological characteristics of cocopith, perlite, vermicullite, vermicompost, sand, rice husk, paddy straw, saw dust and rock wool for using them as substrates for soilless agriculture. The soilless substrates were initially evaluated for pH and EC, and then estimated for total organic carbon by dry combustion method, total nitrogen by Kjeldahl digestion method, potassium by atomic absorption and phosphorus by colorimetric method. The hydrological properties of substrates were estimated by Keen-Rackzowski box method. The desirable level of physical properties of-3 bulk density (0.47 gm cm), particle density (0.63 gm-3 cm), total porosity (75.81%) and chemical properties of-1 pH (6.23), EC (5.02 dS m), total organic carbon (36.39 %), and other properties were noticed under cocopith. The maximum level of water holding capacity (769.30 %) and volume of expansion (185.78 %) was registered by cocopith. Cocopith has favourable hydrological properties with desirable level of physical and chemical properties, which makes it the best medium for soilless agriculture. Coconut fiber is a characteristic natural fiber from the external husk of coconut and its extraction process also without polluting nature.
Aequationes Mathematicae, 1990
Summary In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to... more Summary In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljević, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c ∈ R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca′: a,
Acta Mathematica Hungarica, 1991
The paper describes some basic properties of a class of module maps of Hilbert C,-module, adjoint... more The paper describes some basic properties of a class of module maps of Hilbert C,-module, adjointable operator. 1
Glasnik Matematicki, 2003
Abstract. Let C be the category consisting of Hilbert C,-algebras as well as of the corresponding... more Abstract. Let C be the category consisting of Hilbert C,-algebras as well as of the corresponding linking algebras are also discussed.
Let H be a complex Hilbert space, dim H>1, and let A subuline B(H) be a C*-algebra such that t... more Let H be a complex Hilbert space, dim H>1, and let A subuline B(H) be a C*-algebra such that the ideal K(H) of all compact operators on H is contained in A. Let X be a Hilbert C*-module over A. We prove that any function F:X-->X which preserves the absolute value of the A-valued inner product on X is of
Real Analysis Exchange, 1996
We analyse an algorithm of transition between Cauchy problems for secondorder wave equations and ... more We analyse an algorithm of transition between Cauchy problems for secondorder wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the standard conditions guaranteeing well-posedness. The typical operations involved in rewriting equations into systems are then neither defined classically nor consistently extendible to the distribution theoretic setting. However, employing the nonlinear theory of generalized functions in the sense of Colombeau we arrive at clear statements about the transfer of questions concerning solvability and uniqueness from wave equations to symmetric hyperbolic systems and vice versa. Finally, we illustrate how this transfer method allows to draw new conclusions on unique solvability of the Cauchy problem for wave equations with non-smooth coefficients.
Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators ... more Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators on W are reduced by a suitable Hilbert space contained in W. This enables us to describe bounded E-linear operators by lifting the appropriate results from Hilbert space theory. In particular, generalized compact E-linear operators are characterized.
Journal of Operator Theory, 2008
Revue Roumaine des Mathematiques Pures et Appliquees
Proceedings of the American Mathematical Society
Let W be a Hilbert C*-module over the C*-algebra A ≠ C of all compact operators on a Hilbert spac... more Let W be a Hilbert C*-module over the C*-algebra A ≠ C of all compact operators on a Hilbert space. It is proved that any function T: W → W which preserves the absolute value of the A-valued inner product is of the form Tv = φ(v)Uv, v ∈ W, where φ is a phase function and U is an A-linear isometry. The result generalizes Molnár's extension of Wigner's classical unitary-antiunitary theorem.
Acta Scientiarum Mathematicarum
A theorem of P. A. Fillmore and J. P. Williams [Adv. Math. 7, 254-281 (1971; Zbl 0224.47009)] imp... more A theorem of P. A. Fillmore and J. P. Williams [Adv. Math. 7, 254-281 (1971; Zbl 0224.47009)] implies that a bounded operator A on a separable Hilbert space H is compact if and only if it satisfies lim n Ae n =0, or equivalently, lim n (Ae n |e n )=0 for each orthonormal basis (e n ) for H. In the present note this theorem is reproved using the fact observed by Halmos that each sequence of unit vectors weakly converging to 0 approximately contains an orthonormal subsequence. It is also noted that the stronger version of the theorem remains true, namely without the continuity assumption on A. In the second part of the note the bounded operators for which there exists an orthonormal basis such that either of the above equalities holds are exhibited and completely described.
Journal of Computational Analysis and Applications - J COMPUT ANAL APPL, 2001
We establish a result which subsumes two versions of the extended reversed Meir inequality.
Journal of Mathematical Physics, 2003
Let H be a complex Hilbert space, dim H > 1, and let A ⊆ B(H) be a C *-algebra such that the idea... more Let H be a complex Hilbert space, dim H > 1, and let A ⊆ B(H) be a C *-algebra such that the ideal K(H) of all compact operators on H is contained in A. Let X be a Hilbert C *-module over A. We prove that any function F : X → X which preserves the absolute value of the A-valued inner product on X is of the form F (x) = ϕ(x)U x, x ∈ X, where ϕ is a phase function and U is an A-linear isometry. The result generalizes Wigner's classical unitary-antiunitary theorem and its extension to Hilbert K(H)-modules.
Glasnik Matematicki, 2003
We describe the pullback construction in the category of Hilbert C *-modules (with a suitable cla... more We describe the pullback construction in the category of Hilbert C *-modules (with a suitable class of morphisms) in terms of pullbacks of underlying C *-algebras. In the second section the Busby invariant for extensions of Hilbert C *-modules is introduced and it is proved that each extension is uniquely determined, up to isomorphism, by the corresponding Busby map. The induced extensions of the underlying C *algebras as well as of the corresponding linking algebras are also discussed. The paper ends with a Hilbert C *-module version of a familiar result which states that a C *-algebra is projective if and only if it is corona projective. 2000 Mathematics Subject Classification. 46C50, 46L08. Key words and phrases. Hilbert C *-module, adjointable operator, extension, multiplier algebra.
Journal of Operator Theory, 2001
Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators ... more Let W be a Hilbert H *-module over an H *-algebra E. We show that all bounded E-linear operators on W are reduced by a suitable Hilbert space contained in W. This enables us to describe bounded E-linear operators by lifting the appropriate results from Hilbert space theory. In particular, generalized compact E-linear operators are characterized.
The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1998
An integral inequality is established involving a probability density function on the real line a... more An integral inequality is established involving a probability density function on the real line and its first two derivatives. This generalizes an earlier result of Sato and Watari. If f denotes the probability density function concerned, the inequality we prove is thatunder the conditions β > α 1 and 1/(β+1) < γ ≤ 1.
The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1998
A new version of Jensen's inequality is established for probability distributions on the nonnegat... more A new version of Jensen's inequality is established for probability distributions on the nonnegative real numbers which are characterized by moments higher than the first. We deduce some new sharp bounds for Laplace-Stieltjes transforms of such distribution functions.
To evaluate the physico-chemical and hydrological characteristics of cocopith, perlite, vermicull... more To evaluate the physico-chemical and hydrological characteristics of cocopith, perlite, vermicullite, vermicompost, sand, rice husk, paddy straw, saw dust and rock wool for using them as substrates for soilless agriculture. The soilless substrates were initially evaluated for pH and EC, and then estimated for total organic carbon by dry combustion method, total nitrogen by Kjeldahl digestion method, potassium by atomic absorption and phosphorus by colorimetric method. The hydrological properties of substrates were estimated by Keen-Rackzowski box method. The desirable level of physical properties of-3 bulk density (0.47 gm cm), particle density (0.63 gm-3 cm), total porosity (75.81%) and chemical properties of-1 pH (6.23), EC (5.02 dS m), total organic carbon (36.39 %), and other properties were noticed under cocopith. The maximum level of water holding capacity (769.30 %) and volume of expansion (185.78 %) was registered by cocopith. Cocopith has favourable hydrological properties with desirable level of physical and chemical properties, which makes it the best medium for soilless agriculture. Coconut fiber is a characteristic natural fiber from the external husk of coconut and its extraction process also without polluting nature.
Aequationes Mathematicae, 1990
Summary In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to... more Summary In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljević, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c ∈ R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca′: a,
Acta Mathematica Hungarica, 1991
The paper describes some basic properties of a class of module maps of Hilbert C,-module, adjoint... more The paper describes some basic properties of a class of module maps of Hilbert C,-module, adjointable operator. 1
Glasnik Matematicki, 2003
Abstract. Let C be the category consisting of Hilbert C,-algebras as well as of the corresponding... more Abstract. Let C be the category consisting of Hilbert C,-algebras as well as of the corresponding linking algebras are also discussed.
Let H be a complex Hilbert space, dim H>1, and let A subuline B(H) be a C*-algebra such that t... more Let H be a complex Hilbert space, dim H>1, and let A subuline B(H) be a C*-algebra such that the ideal K(H) of all compact operators on H is contained in A. Let X be a Hilbert C*-module over A. We prove that any function F:X-->X which preserves the absolute value of the A-valued inner product on X is of