scholarly journals Analytic core and quasi-nilpotent part of linear relations in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2499-2515
Author(s):  
Maher Mnif ◽  
Aman-Allah Ouled-Hmeda
Keyword(s):  
Banach Spaces ◽  
Linear Relation ◽  
Linear Relations ◽  
Perturbation Result ◽  
Analytic Core

In this paper, we investigate the notion of analytic core and quasi-nilpotent part of a linear relation. Furthermore, we are interested in studying the set of Generalized Kato linear relations to give some of their properties in connection with the analytic core and the quasi-nilpotent part. We finish by giving a perturbation result for this set of linear relations.

scholarly journals Generalized Kato linear relations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1129-1139 ◽  
Author(s):  
Mohammed Benharrat ◽  
Teresa Álvarez ◽  
Bekkai Messirdi
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Linear Relation ◽  
Shift Operator ◽  
Linear Operators ◽  
Symmetric Difference ◽  
Linear Relations ◽  
Left Shift ◽  
Kato Spectrum

For a Banach space the notions of generalized Kato linear relation and the corresponding spectrum are introduced and studied. We show that the symmetric difference between the generalized Kato spectrum and the Goldberg spectrum of multivalued linear operators in Banach spaces is at most countable. The obtained results are used to describe the generalized Kato spectrum of the inverse of the left shift operator regarded as a linear relation.

scholarly journals The Local spectral theory and surjective spectrum of linear relations

2021 ◽  
Vol 73 (2) ◽  
pp. 222-237
Author(s):  
M. Mnif ◽  
A.-A. Ouled-Hmed
Keyword(s):  
Banach Space ◽  
Spectral Theory ◽  
Linear Relation ◽  
Local Spectrum ◽  
Linear Relations ◽  
Analytic Core ◽  
Local Spectral Theory

UDC 517.98 This paper initiates a study of local spectral theory for linear relations. At the beginning, we define the local spectrum and study its properties. Then we obtain results related to the correlation analytic core and quasinilpotent part of a linear relation in a Banach space . As an application, we give a characterization of the surjective spectrum in terms of the local spectrum and show that if , then does not cluster at .

scholarly journals On strictly quasi-Fredholm linear relations and semi-B-Fredholm linear relation perturbations

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6337-6355 ◽  
Author(s):  
Bouaniza Hafsa ◽  
Maher Mnif
Keyword(s):  
Finite Rank ◽  
Linear Relation ◽  
Linear Relations ◽  
Finite Rank Operators ◽  
Lower Semi ◽  
The Stability

In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent and essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.

scholarly journals Frames for operators in Banach spaces via semi-inner products

2016 ◽  
Vol 14 (03) ◽  
pp. 1650011 ◽  
Author(s):  
Bahram Dastourian ◽  
Mohammad Janfada
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Reproducing Kernel ◽  
Atomic System ◽  
Inner Product ◽  
Reconstruction Formula ◽  
Frame Operator ◽  
Atomic Systems ◽  
Perturbation Result ◽  
Reproducing Kernel Banach Spaces

In this paper, the concept of a family of local atoms in a Banach space is introduced by using a semi-inner product (s.i.p.). Then this concept is generalized to an atomic system for operators in Banach spaces. We also give some characterizations of atomic systems leading to new frames for operators. In addition, a reconstruction formula is obtained. The characterizations of atomic systems allow us to state some results for sampling theory in s.i.p reproducing kernel Banach spaces. Finally, we define the concept of frame operator for these kinds of frames in Banach spaces and then we establish a perturbation result in this framework.

$B$-spectral theory of linear relations in complex Banach spaces

2017 ◽  
Vol 91 (3-4) ◽  
pp. 455-466
Author(s):  
Marcel Roman ◽  
Adrian Sandovici
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Linear Relations

Left-right fredholm and left-right browder linear relations

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 255-271 ◽  
Author(s):  
T. Álvarez ◽  
Fatma Fakhfakh ◽  
Maher Mnif
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Linear Relation ◽  
Finite Rank Operator ◽  
Linear Relations ◽  
Rank Operator ◽  
Type Decomposition ◽  
Converse Results

In this paper we introduce the notions of left (resp. right) Fredholm and left (resp. right) Browder linear relations. We construct a Kato-type decomposition of such linear relations. The results are then applied to give another decomposition of a left (resp. right) Browder linear relation T in a Banach space as an operator-like sum T = A + B, where A is an injective left (resp. a surjective right) Fredholm linear relation and B is a bounded finite rank operator with certain properties of commutativity. The converse results remain valid with certain conditions of commutativity. As a consequence, we infer the characterization of left (resp. right) Browder spectrum under finite rank operator.

Linear Relations Between Higher Matrix Commutators

1964 ◽  
Vol 16 ◽  
pp. 315-320 ◽  
Author(s):  
Nisar A. Khan
Keyword(s):  
Linear Relation ◽  
Closed Field ◽  
Research Papers ◽  
Algebraically Closed Field ◽  
Linear Relations ◽  
Image Position ◽  
Iterated Commutators

Let Mn denote the space of all n-square matrices over an algebraically closed field F. For A, B ∊ Mn, letdefine the iterated commutators of A and B. Recently several research papers (1, 2, 4, and 5) have appeared on these commutators. In (1), Kato and Taussky have proved that for n = 2 the iterated commutators of A and B satisfy the linear relation

Spectral theory of linear relations on real Banach spaces

2007 ◽  
Vol 81 (1-2) ◽  
pp. 15-27 ◽  
Author(s):  
A. G. Baskakov ◽  
A. S. Zagorskii
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Linear Relations
Sign in / Sign up

Export Citation Format

Share Document