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 $M_{*\!\!\!\bigcirc,z}$. 
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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/

[1] H. Alkanjo, “On extended eigenvalues and extended eigenvectors of truncated shift”, Concrete Operators, Versita, 2013, 19–27 | DOI | MR

[2] A. Biswas, A. Lambert S. Petrovic, “Extended eigenvalues and the Volterra operator”, Glasg. Math. J., 44 (2002), 521–534 | DOI | MR | Zbl

[3] S. Brown, “Connections between an operator and a compact operator that yield hyperinvariant subspaces”, J. Operator Theory, 1 (1979), 117–121 | MR | Zbl

[4] A. Lambert, “Hyperinvariant subspaces and extended eigenvalues”, New York J. Math., 10 (2004), 83–88 | MR | Zbl

[5] A. Lambert, S. Petrovic, “Invariant subspaces and limits of similarities”, Acta Sci. Math. (Szeged), 66 (2000), 295–304 | MR | Zbl

[6] V. I. Lomonosov, “Invariant subspaces of the family of operators that commute with a completely continuous operator”, Funkcional. Anal. i Prilozen., 7 (1973), 55–56 (in Russian) | MR

[7] H. Radjavi, P. Rosenthal, Invariant Subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, 77, Springer, New York–Heidelberg, 1973 | MR | Zbl

[8] A. L. Shields, “Weighted shift operators and analytic function theory”, Math. Surveys, 13, A.M.S. Providence, 1974, 49–128 | MR

[9] B. Yousefi, “On the space $\ell^p(\beta)$”, Rend. Circ. Mat. Palermo, 49 (2001), 115–120 | DOI | MR