Korean J. Math. Vol. 25 No. 1 (2017) pp.117-126
DOI: https://doi.org/10.11568/kjm.2017.25.1.117

Subnormality of the weighted Ces\`aro operator $ C_h \in l^2(h) $

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Published: Mar 30, 2017
Keywords:
Extended eigenvalue, Extended eigenoperator, Ces`aro operator
Mathematics Subject Classification:
Primary 47B37, Secondary 47B20, 33D45

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Abderazak Hechifa
Mathematics Department Badji Mokhtar University-Annaba Annaba, Algeria
Abdelouahab Mansour
Operator theory laboratory (LABTHOP) Eloued University El Oued, Algeria

Abstract

The subnormality of some classes of operators is a very interesting property. In this paper, we prove that the weighted Ces\`aro operator $ C_h \in \ell^2(h) $ is subnormal and we described completely the set of the extended eigenvalues for the weighted Ces\`aro operator, some other important results are also given.


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Supporting Agencies

Operator theory laboratory Eloued university Algeria.

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