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

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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...

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Détails bibliographiques
Auteurs principaux:	Elvis Aponte, José Sanabria, Luis Vásquez
Format:	article
Langue:	EN
Publié:	MDPI AG 2021
Sujets:	semi-Fredholm operator property <i>(V<sub>E</sub>)</i> commuting perturbations tensor product Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/8f0a2c9b4eb04d5ea7ff7880b3820510
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Résumé:	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.