Pseudospectra of elements of reduced Banach algebras
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Kulkarni, S. H.
Tusi Math. Research Group (TMRG)
Let 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.
Banach algebra , Direct sum , Reduced Banach algebra , Idempotent , Pseudospectrum , Spectrum
Krishnan, A. and Kulkarni, S. H. (2017) 'Pseudospectra of elements of reduced Banach algebras', Advances in Operator Theory, 2(4), pp. 475-493. doi: 10.22034/aot.1702-1112
© 2017 Tusi Math. Research Group (TMRG)