Teresa Seco - Academia.edu (original) (raw)

Papers by Teresa Seco

Research paper thumbnail of On the Browder essential spectrum of a linear relation

Publicationes Mathematicae Debrecen

Research paper thumbnail of Polynomial in a Saphar linear relation in a Banach space

Filomat, 2017

In this paper, we introduce the notion of Saphar linear relation in a Banach space and we study t... more In this paper, we introduce the notion of Saphar linear relation in a Banach space and we study the behaviour of such notion in polynomials.

Research paper thumbnail of On essentially semi regular linear relations

Linear Algebra and its Applications, 2017

The characterization of bounded essentially semi regular operators in terms of Kato decomposition... more The characterization of bounded essentially semi regular operators in terms of Kato decomposition of finite type was studied by several authors. In this paper, we extend this characterization to the case of essentially semi regular linear relations. We also give other characterization of such linear relations. Further, we apply the obtained results to analyse the stability of the class of essentially semi regular linear relations under additional operator perturbations. Finally, as an application, we get some useful connections between the Fredholm spectrum and the essentially semi regular spectrum of linear relations.

Research paper thumbnail of Coperturbation function and lower semi-Browder multivalued linear operators

Linear and Multilinear Algebra, 2013

ABSTRACT In this article, we investigate the perturbation theory of lower semi-Browder and Browde... more ABSTRACT In this article, we investigate the perturbation theory of lower semi-Browder and Browder linear relations. Our approach is based on the concept of a coperturbation function for linear relations in order to establish some perturbation theorems and deduce the stability under strictly cosingular operator perturbations. Furthermore, we apply the obtained results to study the invariance and the characterization of Browder's essential defect spectrum and Browder's essential spectrum.

Research paper thumbnail of Characterization of Closed Densely Defined Semi-Browder Linear Operators

Complex Analysis and Operator Theory, 2012

In the present paper we characterize the closed densely defined semi-Browder operators through th... more In the present paper we characterize the closed densely defined semi-Browder operators through the Kato decomposition. Furthermore, we apply the obtained results to give a new characterization of Browder's essential defect spectrum and Browder's essential approximate point spectrum under finite rank operator perturbations.

Research paper thumbnail of Quasi-Fredholm linear relations in Hilbert spaces

Filomat, 2017

In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relati... more In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relation in a Hilbert space and we analyze the behaviour of a polynomial in a quasi-Fredholm relation in a Hilbert space.

Research paper thumbnail of On A-Weakly Mpact Operators

Quaestiones Mathematicae

ABSTRACT

Research paper thumbnail of Operator quantities characterizing upper amd lower semi-Fredholm type operators

Research paper thumbnail of Small perturbation of normally solvable relations

Publicationes mathematicae

In the present paper we investigate the stability of the index, the nullity and the defficiency o... more In the present paper we investigate the stability of the index, the nullity and the defficiency of normally solvable linear relations in paracomplete spaces under small perturbation. Results of Kato and of Goldberg about operators in complete spaces are covered.

Research paper thumbnail of Some procedures generating space ideals

Research paper thumbnail of Characterizing two classes of operator ideals

Research paper thumbnail of Stability of isomorphic properties of Banach spaces with respect to the gap

Research paper thumbnail of A Note on Restrictions of Linear Relations

Mathematical Proceedings of the Royal Irish Academy

This note is devoted to the answer to the following question: If X and Y are normed spaces and T ... more This note is devoted to the answer to the following question: If X and Y are normed spaces and T is a linear relation from X into Y such that every closed infinitedimensional subspace M of D(T) contains a closed infinite-dimensional subspace N for which the restriction of T to N is F ' (resp. Tauberian), is T an F ' -relation (resp. Tauberian)? *

Research paper thumbnail of Adjoint characterisations of unbounded weakly compact, weakly completely continuous and unconditionally converging operators

Research paper thumbnail of Relationship Between the Kato Spectrum and the Goldberg Spectrum of a Linear Relation

Mediterranean Journal of Mathematics, 2014

ABSTRACT A classical result of J. Ph. Labrousse (Rev. Roumaine Math. Pures Appl. 25, 1391-1394, 1... more ABSTRACT A classical result of J. Ph. Labrousse (Rev. Roumaine Math. Pures Appl. 25, 1391-1394, 1980) concerning the symmetric difference between the Kato spectrum and the Goldberg spectrum of closed operators in Hilbert spaces is extended to the case of multivalued linear operators in Banach spaces.

Research paper thumbnail of F+ operators and classes associated with some classes of unbounded operators

In this paper we study in a unified way the classes of all weakly compact, weakly completely cont... more In this paper we study in a unified way the classes of all weakly compact, weakly completely continuous, unconditionally converging and Rosenthal operators in relation to a naturally associated class of operators and we generalise certain results of [9] and [10] for unbounded operators acting between normed spaces.

Research paper thumbnail of Spectral Mapping Theorem for Rakocević and Schmoeger Essential Spectra of a Multivalued Linear Operator

Mediterranean Journal of Mathematics, 2014

The purpose of this paper is to investigate a detailed treatment of some subsets of essential spe... more The purpose of this paper is to investigate a detailed treatment of some subsets of essential spectrum and following we will establish the spectral mapping theorems essential approximate point spectrum and defect spectrum of multivalued linear operator.

Research paper thumbnail of A characterization of some subsets of S-essential spectra of a multivalued linear operator

Colloquium Mathematicum, 2014

a heprtment of wthemtisD niversity of yviedoD QQHHUD yviedoD esturisD pinF eEmilX seodunioviFes b... more a heprtment of wthemtisD niversity of yviedoD QQHHUD yviedoD esturisD pinF eEmilX seodunioviFes b,c héprtement de wthémtiquesD niversité de fxD pulté des sienes de fxD oute de soukr um QFSD fF F IIUID QHHHD fxD unisieF b eEmilX mmr ymenVRdyhooFfr c eEmilX erefFteriidfssFrnuFtn Abstract. sn this pper we hrterize some SEessentil spetr of losed liner reltion in terms of ertin liner reltions type semi predholmF Key words: viner reltionsD SEessentil spetrD upper nd lower semi predholm liner reltionsD right nd left predholm liner reltionsF Mathematics Subject Classication: RUeHTF

Research paper thumbnail of Paracomplete normed spaces and Fredholm theory

Rendiconti del Circolo Matematico di Palermo, 1999

ABSTRACT

Research paper thumbnail of Gap formulas for closed linear relations

Mathematical Methods in the Applied Sciences, 2014

Research paper thumbnail of On the Browder essential spectrum of a linear relation

Publicationes Mathematicae Debrecen

Research paper thumbnail of Polynomial in a Saphar linear relation in a Banach space

Filomat, 2017

In this paper, we introduce the notion of Saphar linear relation in a Banach space and we study t... more In this paper, we introduce the notion of Saphar linear relation in a Banach space and we study the behaviour of such notion in polynomials.

Research paper thumbnail of On essentially semi regular linear relations

Linear Algebra and its Applications, 2017

The characterization of bounded essentially semi regular operators in terms of Kato decomposition... more The characterization of bounded essentially semi regular operators in terms of Kato decomposition of finite type was studied by several authors. In this paper, we extend this characterization to the case of essentially semi regular linear relations. We also give other characterization of such linear relations. Further, we apply the obtained results to analyse the stability of the class of essentially semi regular linear relations under additional operator perturbations. Finally, as an application, we get some useful connections between the Fredholm spectrum and the essentially semi regular spectrum of linear relations.

Research paper thumbnail of Coperturbation function and lower semi-Browder multivalued linear operators

Linear and Multilinear Algebra, 2013

ABSTRACT In this article, we investigate the perturbation theory of lower semi-Browder and Browde... more ABSTRACT In this article, we investigate the perturbation theory of lower semi-Browder and Browder linear relations. Our approach is based on the concept of a coperturbation function for linear relations in order to establish some perturbation theorems and deduce the stability under strictly cosingular operator perturbations. Furthermore, we apply the obtained results to study the invariance and the characterization of Browder's essential defect spectrum and Browder's essential spectrum.

Research paper thumbnail of Characterization of Closed Densely Defined Semi-Browder Linear Operators

Complex Analysis and Operator Theory, 2012

In the present paper we characterize the closed densely defined semi-Browder operators through th... more In the present paper we characterize the closed densely defined semi-Browder operators through the Kato decomposition. Furthermore, we apply the obtained results to give a new characterization of Browder's essential defect spectrum and Browder's essential approximate point spectrum under finite rank operator perturbations.

Research paper thumbnail of Quasi-Fredholm linear relations in Hilbert spaces

Filomat, 2017

In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relati... more In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relation in a Hilbert space and we analyze the behaviour of a polynomial in a quasi-Fredholm relation in a Hilbert space.

Research paper thumbnail of On A-Weakly Mpact Operators

Quaestiones Mathematicae

ABSTRACT

Research paper thumbnail of Operator quantities characterizing upper amd lower semi-Fredholm type operators

Research paper thumbnail of Small perturbation of normally solvable relations

Publicationes mathematicae

In the present paper we investigate the stability of the index, the nullity and the defficiency o... more In the present paper we investigate the stability of the index, the nullity and the defficiency of normally solvable linear relations in paracomplete spaces under small perturbation. Results of Kato and of Goldberg about operators in complete spaces are covered.

Research paper thumbnail of Some procedures generating space ideals

Research paper thumbnail of Characterizing two classes of operator ideals

Research paper thumbnail of Stability of isomorphic properties of Banach spaces with respect to the gap

Research paper thumbnail of A Note on Restrictions of Linear Relations

Mathematical Proceedings of the Royal Irish Academy

This note is devoted to the answer to the following question: If X and Y are normed spaces and T ... more This note is devoted to the answer to the following question: If X and Y are normed spaces and T is a linear relation from X into Y such that every closed infinitedimensional subspace M of D(T) contains a closed infinite-dimensional subspace N for which the restriction of T to N is F ' (resp. Tauberian), is T an F ' -relation (resp. Tauberian)? *

Research paper thumbnail of Adjoint characterisations of unbounded weakly compact, weakly completely continuous and unconditionally converging operators

Research paper thumbnail of Relationship Between the Kato Spectrum and the Goldberg Spectrum of a Linear Relation

Mediterranean Journal of Mathematics, 2014

ABSTRACT A classical result of J. Ph. Labrousse (Rev. Roumaine Math. Pures Appl. 25, 1391-1394, 1... more ABSTRACT A classical result of J. Ph. Labrousse (Rev. Roumaine Math. Pures Appl. 25, 1391-1394, 1980) concerning the symmetric difference between the Kato spectrum and the Goldberg spectrum of closed operators in Hilbert spaces is extended to the case of multivalued linear operators in Banach spaces.

Research paper thumbnail of F+ operators and classes associated with some classes of unbounded operators

In this paper we study in a unified way the classes of all weakly compact, weakly completely cont... more In this paper we study in a unified way the classes of all weakly compact, weakly completely continuous, unconditionally converging and Rosenthal operators in relation to a naturally associated class of operators and we generalise certain results of [9] and [10] for unbounded operators acting between normed spaces.

Research paper thumbnail of Spectral Mapping Theorem for Rakocević and Schmoeger Essential Spectra of a Multivalued Linear Operator

Mediterranean Journal of Mathematics, 2014

The purpose of this paper is to investigate a detailed treatment of some subsets of essential spe... more The purpose of this paper is to investigate a detailed treatment of some subsets of essential spectrum and following we will establish the spectral mapping theorems essential approximate point spectrum and defect spectrum of multivalued linear operator.

Research paper thumbnail of A characterization of some subsets of S-essential spectra of a multivalued linear operator

Colloquium Mathematicum, 2014

a heprtment of wthemtisD niversity of yviedoD QQHHUD yviedoD esturisD pinF eEmilX seodunioviFes b... more a heprtment of wthemtisD niversity of yviedoD QQHHUD yviedoD esturisD pinF eEmilX seodunioviFes b,c héprtement de wthémtiquesD niversité de fxD pulté des sienes de fxD oute de soukr um QFSD fF F IIUID QHHHD fxD unisieF b eEmilX mmr ymenVRdyhooFfr c eEmilX erefFteriidfssFrnuFtn Abstract. sn this pper we hrterize some SEessentil spetr of losed liner reltion in terms of ertin liner reltions type semi predholmF Key words: viner reltionsD SEessentil spetrD upper nd lower semi predholm liner reltionsD right nd left predholm liner reltionsF Mathematics Subject Classication: RUeHTF

Research paper thumbnail of Paracomplete normed spaces and Fredholm theory

Rendiconti del Circolo Matematico di Palermo, 1999

ABSTRACT

Research paper thumbnail of Gap formulas for closed linear relations

Mathematical Methods in the Applied Sciences, 2014