Analytic semigroups in Banach algebras and a theorem of Hille

Tadeusz Pytlik

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Displaying similar documents to “Analytic semigroups in Banach algebras and a theorem of Hille”

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We construct two Banach algebras, one which contains analytic semigroups ${(a^{z})}_{R e z > 0}$ such that $| a^{1 + i y} | \to \infty$ arbitrarily slowly as $| y | \to \infty$ , the other which contains ones such that $| a^{1 + i y} | \to \infty$ arbitrarily fast

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Let G be a locally compact group with left Haar measure μ, and let L(G) be the convolution Banach algebra of integrable functions on G with respect to μ. In this paper we are concerned with the investigation of the structure of G in terms of analytic semigroups in L(G).

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A Banach algebra A is said to be topologically nilpotent if $s u p ∥ x ₁ . . . . . . x_{n} ∥^{1 / n} : x_{i} \in A, ∥ x_{i} ∥ \leq 1 (1 \leq i \leq n)$ tends to 0 as n → ∞. We continue the study of topologically nilpotent algebras which was started in [2]

An extremal problem in Banach algebras

Anders Olofsson (2001)

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We study asymptotics of a class of extremal problems rₙ(A,ε) related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative refinements of a theorem of Jan-Erik Björk [1]. In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Björk in [1] is answered in the negative.

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A properly infinite C*-algebra has no non-zero traces. We construct properly infinite Banach *-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly "close" to the class of C*-algebras, in the sense that they can be hermitian or *-semisimple.

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Dual Banach algebras: representations and injectivity

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We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of...

Banach-Stone Theorems for Banach Manifolds.

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On Cohen's proof of the Factorization Theorem

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