The Banach algebra generated by a contraction期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The Banach algebra generated by a contraction

Authors:	H. S. Mustafayev

Affiliation:	Department of Mathematics, Faculty of Arts and Sciences, Yüzüncü Yil University, 65080, Van, Turkey

Abstract:	Let be a contraction on a Banach space and $A_{T}$ the Banach algebra generated by . Let $sigma _{u}(T)$ be the unitary spectrum (i.e., the intersection of with the unit circle) of . We prove the following theorem of Katznelson-Tzafriri type: If $sigma _{u}(T)$ is at most countable, then the Gelfand transform of $Rin A_{T}$ vanishes on $sigma _{u}(T)$ if and only if $lim_{nrightarrow infty }leftVert T^{n}RrightVert =0.$

Keywords:	Contraction Banach algebra spectrum semisimplicity

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