B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch; H. Zguitti

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 1, page 39-49
  • ISSN: 0862-7959

Abstract

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Let X be a Banach space and T be a bounded linear operator on X . We denote by S ( T ) the set of all complex λ ∈ ℂ such that T does not have the single-valued extension property at λ . In this note we prove equality up to S ( T ) between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.

How to cite

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Amouch, M., and Zguitti, H.. "B-Fredholm and Drazin invertible operators through localized SVEP." Mathematica Bohemica 136.1 (2011): 39-49. <http://eudml.org/doc/197058>.

@article{Amouch2011,
abstract = {Let $X$ be a Banach space and $T$ be a bounded linear operator on $X$. We denote by $S(T)$ the set of all complex $\lambda \in \mathbb \{C\}$ such that $T$ does not have the single-valued extension property at $\lambda $. In this note we prove equality up to $S(T)$ between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.},
author = {Amouch, M., Zguitti, H.},
journal = {Mathematica Bohemica},
keywords = {B-Fredholm operator; Drazin invertible operator; single-valued extension property; B-Fredholm operator; Drazin invertible operator; single-valued extension property (SVEP); generalised Weyl's theorem},
language = {eng},
number = {1},
pages = {39-49},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {B-Fredholm and Drazin invertible operators through localized SVEP},
url = {http://eudml.org/doc/197058},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Amouch, M.
AU - Zguitti, H.
TI - B-Fredholm and Drazin invertible operators through localized SVEP
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 1
SP - 39
EP - 49
AB - Let $X$ be a Banach space and $T$ be a bounded linear operator on $X$. We denote by $S(T)$ the set of all complex $\lambda \in \mathbb {C}$ such that $T$ does not have the single-valued extension property at $\lambda $. In this note we prove equality up to $S(T)$ between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.
LA - eng
KW - B-Fredholm operator; Drazin invertible operator; single-valued extension property; B-Fredholm operator; Drazin invertible operator; single-valued extension property (SVEP); generalised Weyl's theorem
UR - http://eudml.org/doc/197058
ER -

References

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