Michael Lambrou - Academia.edu (original) (raw)

Papers by Michael Lambrou

If K,L and M are (closed) subspaces of a Banach space X sat- isfying K \ M = (0), K _ L = X and L... more If K,L and M are (closed) subspaces of a Banach space X sat- isfying K \ M = (0), K _ L = X and L M, then P = {(0),K,L,M,X} is a pentagon subspace lattice on X. If P1 and P2 are pentagons, every (al- gebraic) isomorphism ' : AlgP1 ! AlgP2 is quasi-spatial. The SOT-closure of the fin-

ABSTRACT This set of notes on Mathematical induction is a continuation of an earlier part which a... more ABSTRACT This set of notes on Mathematical induction is a continuation of an earlier part which appeared in the same journal. The present part contains less routine techniques of induction than the ones normally found in a standard school textbook.

ABSTRACT Incluye bibliografía

Contemporary Mathematics, 1991

This set of notes on Mathematical induction is a continuation of an earlier part which appeared i... more This set of notes on Mathematical induction is a continuation of an earlier part which appeared in the same journal. The present part contains less routine techniques of induction than the ones normally found in a standard school textbook.

Indiana University Mathematics Journal

In this paper we present the story of the most famous ancient female math-ematician, Hypatia, and... more In this paper we present the story of the most famous ancient female math-ematician, Hypatia, and her father Theon of Alexandria. The mathematician and philosopher Hypatia flourished in Alexandria from the second part of the 4 th century until her violent death incurred by a mob in 415. She was the daughter of Theon of Alexandria, a math-ematician and astronomer, who flourished in Alexandria during the second part of the fourth century. Information on Theon's life is only brief, coming mainly from a note in the Suda (Suida's Lexicon, written about 1000 AD) stating that he lived in Alexandria in the times of Theodosius I (who reigned AD 379-395) and taught at the Museum. He is, in fact, the Museum's last attested member. Descriptions of two eclipses he observed in Alexandria included in his commentary to Ptolemy's Mathematical Syntaxis (Almagest) and elsewhere have been dated as the eclipses that occurred in AD 364, which is consistent with Suda. Although originality ...

JOURNAL OF OPERATOR THEORY

Proceedings of the American Mathematical Society, 1991

An operator on a separable Hubert space is called bitriangular if it and its adjoint have upper t... more An operator on a separable Hubert space is called bitriangular if it and its adjoint have upper triangular representations with respect to two (perhaps different) orthonormal bases. Although bitriangular operators have some tractable properties and seem to be the right context for generalization of matrices to infinite dimensions, we give counterexamples to various open problems regarding this class of operators. The counterexamples make use of a property that an M-basis may or may not have.

Memoirs of the American Mathematical Society, 1991

Linear Algebra and its Applications, 1990

Linear Algebra and its Applications, 2002

A family F of subspaces of a finite-dimensional Hilbert space H is transitive if every operator l... more A family F of subspaces of a finite-dimensional Hilbert space H is transitive if every operator leaving every element of F invariant is scalar. If dim H 3, the minimum cardinality of a transitive family is 4. All 4-element transitive families of subspaces of 3-dimensional space are described. For spaces of dimension greater than 3, necessary, but not sufficient, conditions satisfied by every 4-element transitive family are obtained, showing that (i) either every pair of subspaces intersects in (0) or every pair spans H (but not both), (ii) at least three of the subspaces must have the same dimension (either [dim H/2] or [dim H/2] + 1), the dimension of the remaining subspace differing from this common dimension by at most 1.

Journal of Mathematical Analysis and Applications, 1997

The spatial action of the Stone-type spectral family for a certain type of strongly continuous on... more The spatial action of the Stone-type spectral family for a certain type of strongly continuous one-parameter groups of surjective isometries, as well as of the spectral decomposition of their single elements on c , 1 F p F ϱ, is examined. The UMD p structure, for 1p-ϱ, and triangular truncations and duality for p s 1, ϱ are involved. In various cases, concrete descriptions of the associated Riesz᎐Nagy operators and Arveson's spectral subspaces are derived as byproducts of independent interest.

Journal of the London Mathematical Society, 1992

Let D = {(0), K, L, M, X) be a double triangle subspace lattice on a nonzero complex reflexive Ba... more Let D = {(0), K, L, M, X) be a double triangle subspace lattice on a nonzero complex reflexive Banach space X. We show that Alg D contains a non-zero finite rank operator if and only if both of the linear manifolds K! (L + M) and K 1 !(L 1 + M l) are non-zero. Every non-zero finite rank operator of Alg D has even rank and is a finite sum of rank two operators of Alg D. For every natural number l there exists a double triangle whose Alg contains operators of rank 2l but none of higher finite rank. The lattice of invariant subspaces of the algebra of finite rank operators of Alg D is described. A sufficient condition for the semisimplicity of Alg D, and a necessary condition for its semiprimeness are given. The latter condition need not be satisfied so there exists a double triangle whose Alg is not semiprime.

Integral Equations and Operator Theory, 1993

ABSTRACT We study reflexive algebrasA whose invariant lattices LatA are generated by M-bases of 2... more ABSTRACT We study reflexive algebrasA whose invariant lattices LatA are generated by M-bases of 2. Examples are given whereA differs from ( being the rank one subalgebra ofA), and where together with the identity I is not strongly dense inA. For M-bases in a special class, we characterize the cases when they are strong, and also when the identity I is the ultraweak limit of a sequence of contractions in . We show that this holds provided that I is approximable by compact operators inA at any two points of 2. We show that the spaceA+* (where is the annihilator of ) is ultraweakly dense in (2), and characterize the M-bases in this class for which the sum is direct. We give a class of automorphisms ofA which are strongly continuous but not spatial.

Bulletin of the London Mathematical Society, 1980

Bulletin of the Australian Mathematical Society, 2009

The length of every pair {A,B} of 6×6 complex matrices is shown to be at most 10, that is, the wo... more The length of every pair {A,B} of 6×6 complex matrices is shown to be at most 10, that is, the words in A,B of length at most 10, including the empty word, span the unital algebra generated by A,B. This supports the conjecture that the length of every pair of n×n complex matrices is at most 2n−2, known to be true for n<6.

Proceedings of the American Mathematical Society, Apr 1, 1994

Two subspaces M and N of a Hilbert space H are in generalized generic position if MnN = A/x n N1-... more Two subspaces M and N of a Hilbert space H are in generalized generic position if MnN = A/x n N1-= (0) and dimfA/-1 n N) = dim(M D N1-). If H is separable and both the pairs {M\, Nx} and {A/2, N2} are in generalized generic position, then every algebraic isomorphism (/> : Alg{A/i, Nx}-» Alg{A/2, N2} is spatially induced, that is, there exists an invertible operator To € 3S(H) such that <p(B) = TqBTq1 , for every B 6 Mg{Mx, Nx}. The proof of this uses the following result: If H is separable, Jf Ç H is a proper operator range in H, and the operator T € 3S{K) has the property that, for every W £ SS^H") leaving J! invariant, the range of WT-TW is included in J! , then the range of T-X is included in JÍ , for some unique scalar X .