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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
Abstract:
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 $M_{*\!\!\!\bigcirc,z}$.
Keywords and phrases:
Cauchy product, extended eigenvalue, multiplication operators.
Received: 13.01.2019
Citation:
Y. Estaremi, “Generalized Cauchy product and related operators on $\ell^p(\beta)$”, Eurasian Math. J., 12:2 (2021), 19–24
Linking options:
https://www.mathnet.ru/eng/emj400 https://www.mathnet.ru/eng/emj/v12/i2/p19
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