Geodesic
On the Radicals of Algebras Generated by a Contraction
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 80-84.

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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. 
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H. S. Mustafaev. On the Radicals of Algebras Generated by a Contraction. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 80-84. http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a9/

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