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Generalized Cauchy product and related operators on $\ell^p(\beta)$
Y. Estaremi Department of Mathematics and Computer Sciences,
Golestan University,
Gorgan, Iran
Аннотация:
In this paper first we give some necessary and sufficient conditions for the boundedness of the multiplication operator $D_f=M_{*\!\!\!\bigcirc,f}$ with respect to the generalized Cauchy product $*\!\!\!\!\!\bigcirc$, on $\ell^p(\beta)$. Also, under certain conditions, we give the characterization of the extended eigenvalues and extended eigenvectors of the multiplication operator $M_{*\!\!\!\bigcirc,z}$ on $\ell^p(\beta)$. Finally we describe the commutants of $M_{*\!\!\!\bigcirc,z}$ and consequently the collection of all hyperinvariant subspaces of $M_{*\!\!\!\bigcirc,z}$.
Ключевые слова и фразы:
Cauchy product, extended eigenvalue, multiplication operators.
Поступила в редакцию: 13.01.2019
Образец цитирования:
Y. Estaremi, “Generalized Cauchy product and related operators on $\ell^p(\beta)$”, Eurasian Math. J., 12:2 (2021), 19–24
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj400 https://www.mathnet.ru/rus/emj/v12/i2/p19
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Страница аннотации: | 164 | PDF полного текста: | 136 | Список литературы: | 23 |
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