Characterization of some Classes Related to the Class of Browder Linear Relations

doi:10.17398/2605-5686.33.2.191

Authors

  • Attaif Farah Department of Mathematics, Faculty of Science of Sfax, University of Sfax Soukra Road, Km 3.5, PO Box 1171, 3000, Sfax, Tunisia
  • Maher Mnif Department of Mathematics, Faculty of Science of Sfax, University of Sfax Soukra Road, Km 3.5, PO Box 1171, 3000, Sfax, Tunisia

Keywords:

Closed linear relation, left- and right-Browder linear relation, left and right invertible linear relation

Abstract

In this paper, we introduce the sets of left and right invertible linear relations and we give some of their properties. Furthermore, we study the connection between these sets and the classes of Fredholm linear relations. The obtained results are used to give some characterizations of some classes related to the class of Browder linear relations.

Downloads

Download data is not yet available.

References

T. Alvarez, On Regular Linear Relations, Acta Math. Sin. (Engl. Ser.) 28 (1) (2012), 183 – 194.

T. Alvarez, On the perturbation of semi-Fredholm relations with complemented ranges and null spaces, Acta Math. Sin. (Engl. Ser.) 26 (8) (2010), 1545 – 1554. Published online: July 15, 2010.

T. Alvarez, M. Benharrat, Relationship Between the Kato Spectrum and the Goldberg Spectrum of a Linear Relation, Mediterr. J. Math. 13 (1) (2016), 365 – 378.

T. Alvarez, D. Wilcox, Perturbation theory of multivalued Atkinson operators in normed spaces, Bull. Austral. Math. Soc. 76 (2) (2007), 195 – 204.

T. Alvarez, Y. Chamkha, M. Mnif, Left- and right-Atkinson linear relation matrices, Mediterr. J. Math. 13 (4) (2016), 2039 – 2059.

T. Alvarez, F. Fakhfakh, M. Mnif, Coperturbation function and lower semi-Browder multivalued linear operators, Linear Multilinear Algebra 61 (4) (2013), 494 – 516.

T. Alvarez, F. Fakhfakh, M. Mnif, Left-right Fredholm and left-right Browder linear relations, Filomat 31 (2) (2017), 255 – 271.

R.W. Cross, “ Multivalued Linear Operators ”, Monographs and Textbooks in Pure and Applied Mathematics, 213. Marcel Dekker, Inc., New York, 1998.

F. Fakhfakh, M. Mnif, Perturbation theory of lower semi-Browder multivalued linear operators, Publ. Math. Debrecen 78 (3-4) (2011), 595 – 606.

V. Müller, “ Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras ”, Second edition, Operator Theory: Advances and Applications, 139. Birkhäuser Verlag, Basel, 2007.

C. Snezana Zivkovic-Zlatanovic, Dragan S. Djordjevic, Robin E. Harte, On left and right Browder operators, J. Korean Math. Soc. 48 (5) (2011), 1053 – 1063.

D. Wilcox, Essential spectra of linear relations, Linear Algebra Appl. 462 (2014), 110 – 125.

Downloads

Published

2018-12-01

Issue

Section

Operator Theory

How to Cite

Characterization of some Classes Related to the Class of Browder Linear Relations: doi:10.17398/2605-5686.33.2.191. (2018). Extracta Mathematicae, 33(2), 191-208. https://revista-em.unex.es/index.php/EM/article/view/2605-5686.33.2.191