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On a certain class of subspectra

Andrzej Sołtysiak (1991)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting n -tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

Rafeiro, Humberto, Samko, Stefan (2007)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ = f, known as the generalized...

On a class of inner maps

Edoardo Vesentini (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let f be a continuous map of the closure Δ ¯ of the open unit disc Δ of C into a unital associative Banach algebra A , whose restriction to Δ is holomorphic, and which satisfies the condition whereby 0 σ f z Δ ¯ for all z Δ and σ f z Δ whenever z Δ (where σ x is the spectrum of any x A ). One of the basic results of the present paper is that f is , that is to say, σ f z is then a compact subset of Δ that does not depend on z for all z Δ ¯ . This fact will be applied to holomorphic self-maps of the open unit ball of some J * -algebra...

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