An Analogue of the Spectral Mapping Theorem for Condition Spectrum

Kumar, G. Krishna; Kulkarni, S. H.

doi:10.1007/978-3-0348-0648-0_19

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2019

2023

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Cited by 5 publications

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“…Also in some situations, if (A, (p k )) is a commutative Fréchet Q-algebra with unit e A and ε > 0, then for every x ∈ A and λ ∈ σ ε (x), there exists weakly almost multiplicative map T : A → C such that T(x) = λ and T(e A ) = 1. In [13], the authors have given an analogue of the Spectral Mapping Theorem for condition spectrum. The ε−spectrum is a useful tool in the numerical solution of operator equations.…”

Section: Introductionmentioning

confidence: 99%

Almost multiplicative maps and ε-spectrum of an element in Fréchet Q-algebra

Farajzadeh

Omidi

2019

Filomat

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Let (A, (p k)) be a Fréchet Q-algebra with unit e A. The ε− spectrum of an element x in A is defined by σ ε (x) = {λ ∈ C : p k 0 (λe A − x)p k 0 (λe A − x) −1 ≥ 1 ε } for 0 < ε < 1. We show that there is a close relation between the ε−spectrum and almost multiplicative maps. It is also shown that {ϕ(x) : ϕ ∈ M ε alm (A), ϕ(e A) = 1} ⊆ σ ε (x) for every x ∈ A, where M ε alm (A) is the set of all ε− multiplicative maps from A to C.

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Section: Introductionmentioning

confidence: 99%