Open Access
Autumn 2017 Pseudospectra of elements of reduced Banach algebras
Arundhathi Krishnan, S. H. Kulkarni
Adv. Oper. Theory 2(4): 475-493 (Autumn 2017). DOI: 10.22034/aot.1702-1112


Let $A$ be a Banach algebra with identity $1$ and $p \in A$ be a non-trivial idempotent. Then $q=1-p$ is also an idempotent. The subalgebras $pAp$ and $qAq$ are Banach algebras, called reduced Banach algebras, with identities $p$ and $q$ respectively. For $a \in A$ and $\varepsilon > 0$, we examine the relationship between the $\varepsilon$-pseudospectrum $\Lambda_{\varepsilon}(A,a)$ of $a \in A$, and $\varepsilon$-pseudospectra of $pap \in pAp$ and $qaq \in qAq$. We also extend this study by considering a finite number of idempotents $p_{1},\cdots,p_{n}$, as well as an arbitrary family of idempotents satisfying certain conditions.


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Arundhathi Krishnan. S. H. Kulkarni. "Pseudospectra of elements of reduced Banach algebras." Adv. Oper. Theory 2 (4) 475 - 493, Autumn 2017.


Received: 3 February 2017; Accepted: 12 July 2017; Published: Autumn 2017
First available in Project Euclid: 4 December 2017

zbMATH: 06804223
MathSciNet: MR3730042
Digital Object Identifier: 10.22034/aot.1702-1112

Primary: 47A10
Secondary: 46H05 , 47A12

Keywords: direct sum , idempotent , pseudospectrum , reduced Banach algebra , spectrum

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.2 • No. 4 • Autumn 2017
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