Geodesic
Generalized Cauchy product and related operators on $\ell^p(\beta)$
Eurasian mathematical journal, Tome 12 (2021) no. 2, pp. 19-24

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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 $M_{*\!\!\!\bigcirc,z}$. 
@article{EMJ_2021_12_2_a2,
     author = {Y. Estaremi},
     title = {Generalized {Cauchy} product and related operators on $\ell^p(\beta)$},
     journal = {Eurasian mathematical journal},
     pages = {19--24},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2021_12_2_a2/}
}
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Y. Estaremi. Generalized Cauchy product and related operators on $\ell^p(\beta)$. Eurasian mathematical journal, Tome 12 (2021) no. 2, pp. 19-24. http://geodesic.mathdoc.fr/item/EMJ_2021_12_2_a2/