Essentially hyponormal operators with essential spectrum contained in a circle

In this paper two results are given . It is proved that if the essential spectrum σ(π(T)) of the bounded hyponormal operator T is contained in a circle, then T is essentially normal operator. Based on this result it is proved that if <...

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Main Authors:	Shquipe I. Lohaj, Muhib R. Lohaj
Format:	Article
Language:	English
Published:	Università degli Studi di Catania 2009-05-01
Series:	Le Matematiche
Subjects:	Essentiall spectrum Quasidiagonal operator
Online Access:	http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/246

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spelling	doaj-18a14d83690c4da280516b434967c08d2020-11-25T03:43:01ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982009-05-016419396223Essentially hyponormal operators with essential spectrum contained in a circleShquipe I. LohajMuhib R. LohajIn this paper two results are given . It is proved that if the essential spectrum <em>σ(π(T))</em> of the bounded hyponormal operator <em>T</em> is contained in a circle, then <em>T</em> is essentially normal operator. Based on this result it is proved that if <em>T∈ L(H)</em> with ind<em> T = 0</em> then<em> T = λU + K</em> (where <em>λ ∈ R^+, U</em> is a unitary operator and <em>K</em> is a compact operator) if and only if <em>TT</em>^∗ is quasi-diagonal with respect to any sequence<em> {P_n }</em> in <em>PF(H)</em> such that <em>Pn → I</em>, strongly.<br /><br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/246Essentiall spectrumQuasidiagonal operator
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Shquipe I. Lohaj Muhib R. Lohaj
spellingShingle	Shquipe I. Lohaj Muhib R. Lohaj Essentially hyponormal operators with essential spectrum contained in a circle Le Matematiche Essentiall spectrum Quasidiagonal operator
author_facet	Shquipe I. Lohaj Muhib R. Lohaj
author_sort	Shquipe I. Lohaj
title	Essentially hyponormal operators with essential spectrum contained in a circle
title_short	Essentially hyponormal operators with essential spectrum contained in a circle
title_full	Essentially hyponormal operators with essential spectrum contained in a circle
title_fullStr	Essentially hyponormal operators with essential spectrum contained in a circle
title_full_unstemmed	Essentially hyponormal operators with essential spectrum contained in a circle
title_sort	essentially hyponormal operators with essential spectrum contained in a circle
publisher	Università degli Studi di Catania
series	Le Matematiche
issn	0373-3505 2037-5298
publishDate	2009-05-01
description	In this paper two results are given . It is proved that if the essential spectrum <em>σ(π(T))</em> of the bounded hyponormal operator <em>T</em> is contained in a circle, then <em>T</em> is essentially normal operator. Based on this result it is proved that if <em>T∈ L(H)</em> with ind<em> T = 0</em> then<em> T = λU + K</em> (where <em>λ ∈ R^+, U</em> is a unitary operator and <em>K</em> is a compact operator) if and only if <em>TT</em>^∗ is quasi-diagonal with respect to any sequence<em> {P_n }</em> in <em>PF(H)</em> such that <em>Pn → I</em>, strongly.<br /><br />
topic	Essentiall spectrum Quasidiagonal operator
url	http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/246
work_keys_str_mv	AT shquipeilohaj essentiallyhyponormaloperatorswithessentialspectrumcontainedinacircle AT muhibrlohaj essentiallyhyponormaloperatorswithessentialspectrumcontainedinacircle
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Essentially hyponormal operators with essential spectrum contained in a circle

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