2024-10-012024-10-012017Krishnan, A. and Kulkarni, S. H. (2017) 'Pseudospectra of elements of reduced Banach algebras', Advances in Operator Theory, 2(4), 475-493, available: http://doi.org/10.22034/aot.1702-1112.2538-225xhttps://dspace.mic.ul.ie/handle/10395/3335Let A be a Banach algebra with identity 1 and p ∈ 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 ∈ A and ε > 0, we examine the relationship between the ε-pseudospectrum Λε(A, a) of a ∈ A, and ε-pseudospectra of pap ∈ pAp and qaq ∈ qAq. We also extend this study by considering a finite number of idempotents p1, · · · , pn, as well as an arbitrary family of idempotents satisfying certain conditions.eng12 monthshttp://www.aot-math.org/article_48321.htmlDirect sumReduced Banach algebraIdempotentPseudospectrumSpectrumArticle10.22034/aot.1702-1112