Brief communications

On the Radicals of Algebras Generated by a Contraction

H. S. Mustafaev

Yuzuncu Yil University, Turkey

Abstract: Let $T$ be a contraction on a Banach space, and let $A_{T}$ ($W_{T}$) be the closure in the uniform (respectively, in the weak) operator topology of the set of all polynomials in $T$. The asymptotic behavior of the radicals of the algebras $A_{T}$ and $W_{T}$ is studied.

Keywords: Banach space, contraction, spectrum, local spectrum, radical.

UDC: 517.98

Received: 15.07.2009

DOI: 10.4213/faa2998

 English version: Functional Analysis and Its Applications, 2010, 44:3, 226–229

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