Displaying similar documents to “On the Gelfand-Hille theorems”

On the differences of the consecutive powers of Banach algebra elements

Helmuth Rönnefarth (1997)

Banach Center Publications

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Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence x n ( x - 1 ) n ∈ ℕ for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of x n n ∈ ℕ and 1 / n ∑ k = 0 n - 1 x k n ∈ ℕ .

Functions of operators and their commutators in perturbation theory

Yu. Farforovskaya (1994)

Banach Center Publications

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This paper shows some directions of perturbation theory for Lipschitz functions of selfadjoint and normal operators, without giving precise proofs. Some of the ideas discussed are explained informally or for the finite-dimensional case. Several unsolved problems are mentioned.

Distances between composition operators.

Valentin Matache (2007)

Extracta Mathematicae

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Composition operators C induced by a selfmap φ of some set S are operators acting on a space consisting of functions on S by composition to the right with φ, that is Cf = f º φ. In this paper, we consider the Hilbert Hardy space H on the open unit disk and find exact formulas for distances ||C - C|| between composition operators. The selfmaps φ and ψ involved in those formulas are constant, inner, or analytic selfmaps of the unit disk fixing the origin.

Local spectrum and Kaplansky's theorem on algebraic operators

Driss Drissi (1998)

Colloquium Mathematicae

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Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.