Perturbation Theory for Property (<i>V</i><i><sub>E</sub></i>) and Tensor Product

Perturbation Theory for Property (<i>V</i><i><sub>E</sub></i>) and Tensor Product

Given a complex Banach space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula>, we investigate the stable chara...

Full description

Saved in:
Bibliographic Details
Main Authors: Elvis Aponte, José Sanabria, Luis Vásquez
Format: article
Language:EN
Published: MDPI AG 2021
Subjects:
semi-Fredholm operator
property <i>(V<sub>E</sub>)</i>
commuting perturbations
tensor product
Mathematics
QA1-939
Online Access:https://doaj.org/article/8f0a2c9b4eb04d5ea7ff7880b3820510
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Given a complex Banach space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula>, we investigate the stable character of the property <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>V</mi><mi>E</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> for a bounded linear operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mo>:</mo><mi mathvariant="script">X</mi><mo>→</mo><mi mathvariant="script">X</mi></mrow></semantics></math></inline-formula>, under commuting perturbations that are Riesz, compact, algebraic and hereditarily polaroid. We also analyze sufficient conditions that allow the transfer of property <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>V</mi><mi>E</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> from the tensorial factors <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">T</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula> to its tensor product.

Similar Items