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Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1

If T or T∗ is an algebraically wF(p,r,q) operator with p,r>0 and q≥1 acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for f(T), for every f∈Hol(σ(T)), where Hol(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Mor...

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Main Author:	Rashid, M.H.M.
Format:	Article
Language:	English
Published:	Інститут математики НАН України 2011
Series:	Український математичний журнал
Subjects:	Статті
Online Access:	http://dspace.nbuv.gov.ua/handle/123456789/166357
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spelling	irk-123456789-1663572020-02-20T01:26:34Z Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1 Rashid, M.H.M. Статті If T or T∗ is an algebraically wF(p,r,q) operator with p,r>0 and q≥1 acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for f(T), for every f∈Hol(σ(T)), where Hol(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T∗ is a wF(p,r,q) operator with p,r>0 and q≥1, then the a-Weyl theorem holds for f(T). Also, if T or T∗ is an algebraically wF(p,r,q) operators with p,r>0 and q≥1, then we establish spectral mapping theorems for the Weyl spectrum and essential approximate point spectrum of T for every f∈Hol(σ(T)), respectively. Finally, we examine the stability of the Weyl theorem and a-Weyl theorem under commutative perturbation by finite-rank operators. У випадку, коли T або T∗ — оператори, що алгебраїчно належать класу wF(p,r,q), де p,r>0,q≥1i дiють на нескiнченновимiрному сепарабельному гiльбертовому просторi, доведено, що теорема Вейля виконується для f(T) при кожному f∈Hol(σ(T)), де Hol(σ(T)) — множина всiх аналiтичних функцiй у вiдкритому околi σ(T). Крiм того, якщо T∗ — оператор класу wF(p,r,q), де p,r>0 i q≥1, то a-теорема Вейля виконується для f(T). У випадку, коли T або T∗ — оператори, що алгебраїчно належать класу wF(p,r,q) при p,r>0 i q≥1, встановлено теореми про спектральне вiдображення, вiдповiдно, для спектра Вейля та для iстотного наближеного точкового спектра оператора T для кожного f∈Hol(σ(T)). Дослiджено стiйкiсть теореми Вейля та a-теореми Вейля при комутативному збуреннi операторами скiнченного рангу. 2011 Article Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1 / M.H.M. Rashid // Український математичний журнал. — 2011. — Т. 63, № 8. — С. 1092–1102. — Бібліогр.: 25 назв. — англ. 1027-3190 http://dspace.nbuv.gov.ua/handle/123456789/166357 517.9 en Український математичний журнал Інститут математики НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Статті Статті
spellingShingle	Статті Статті Rashid, M.H.M. Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1 Український математичний журнал
description	If T or T∗ is an algebraically wF(p,r,q) operator with p,r>0 and q≥1 acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for f(T), for every f∈Hol(σ(T)), where Hol(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T∗ is a wF(p,r,q) operator with p,r>0 and q≥1, then the a-Weyl theorem holds for f(T). Also, if T or T∗ is an algebraically wF(p,r,q) operators with p,r>0 and q≥1, then we establish spectral mapping theorems for the Weyl spectrum and essential approximate point spectrum of T for every f∈Hol(σ(T)), respectively. Finally, we examine the stability of the Weyl theorem and a-Weyl theorem under commutative perturbation by finite-rank operators.
format	Article
author	Rashid, M.H.M.
author_facet	Rashid, M.H.M.
author_sort	Rashid, M.H.M.
title	Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1
title_short	Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1
title_full	Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1
title_fullStr	Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1
title_full_unstemmed	Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1
title_sort	weyl's theorem for algebrascally wf(p,r,q) operators with p,q>0 and q≥1
publisher	Інститут математики НАН України
publishDate	2011
topic_facet	Статті
url	http://dspace.nbuv.gov.ua/handle/123456789/166357
citation_txt	Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1 / M.H.M. Rashid // Український математичний журнал. — 2011. — Т. 63, № 8. — С. 1092–1102. — Бібліогр.: 25 назв. — англ.
series	Український математичний журнал
work_keys_str_mv	AT rashidmhm weylstheoremforalgebrascallywfprqoperatorswithpq0andq1
first_indexed	2023-10-18T22:18:16Z
last_indexed	2023-10-18T22:18:16Z
_version_	1796155165913382912

Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1

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