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) $

Abderazak Hechifa, Abdelouahab Mansour


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.


Extended eigenvalue, Extended eigenoperator, Ces`aro operator

Subject classification

Primary 47B37; Secondary 47B20, 33D45


Operator theory laboratory, Eloued university, Algeria.

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Animikh Biswas, Alan Lambert and SrdjanPetrovic. Extended eigenvalues and the Volterra operator. Glasg. math. J. 44 (3) (2002), 521–534. (Google Scholar)

Animikh Biswas and Srdjan Petrovic. On extended eigenvalues of operators. Integral Equtions Operator Theory 55 (2) (2006), 233–248. (Google Scholar)

Paul S. Bourdon and Joel H. Shapiro. Intertwining relations and extended eigen- values for analytic Toeplitz operators. Illinois J. Math. 52 (3) (2008), 1007–1030. (Google Scholar)

Arlen Brown, P.R.Halmos and A.L.Shields, Ces`aro operators, Acta Sci.Math. (Szeged) 26 (1965), 125–137. (Google Scholar)

P.R. Halmos, A Hilbert Space Problem Book, D. Van Nostrand Company, Inc.Princeton, New Jerse, (1967) . (Google Scholar)

M. Lacruz, F. Saavedra, S. Petrovic and O. Zabeti. Extended eigenvalues for Ces`aro operators, J. Math. Anal. Appl. 429 (2015), 623–657. (Google Scholar)

A. L. Shields and L. J. Wallen. The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1970/1971), 777–788. (Google Scholar)

Tavan T. Trent, New conditions for subnormality, Pacific Journal of Mathematics, Vol. 93, No. 2, April, 1981. (Google Scholar)

Julia Wagner, On the cesro operator in weighted l2sequence space and the generalized concept of normality, Ann. Funct. Anal. 4 (2) (2013), 1–11. (Google Scholar)


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