On some deddens subspaces of Banach algebras
Let A be a Banach algebra with a unit e, and let a ? A be an invertible element. We define the following algebra: Bloca := n {x ? A :??anxa-n?? ? cxn?(x) for some ?(x) ? 0 and cx > 0}. In this articlewestudy some properties of this algebra; in particular, weprove that Bloce+p = {x ? A : px (e-p) = 0}, where p is an idempotent in A. We also investigate the following Deddens subspace. Let a,b ? A be two elements. Fix any number ?,0 ? ? < 1, and consider the following subspace of A : D? a,b := {x ? A : ??anxbn?? = O(n?) as n ? ?}. Here we study some properties of the subspaces D?a,b and D?b,a.
2007 ◽
Vol 83
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pp. 271-284
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2018 ◽
Vol 11
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pp. 1850021
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1967 ◽
Vol 8
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pp. 41-49
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2018 ◽
Vol 17
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pp. 1850169
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1959 ◽
Vol 11
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pp. 297-310
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2001 ◽
Vol 6
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pp. 138-146
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1988 ◽
Vol 44
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pp. 143-145
1985 ◽
Vol 37
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pp. 664-681
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