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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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/166357 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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