Displaying similar documents to “Functional calculus and the Gelfand transformation”

Banach-valued axiomatic spectra

S. Seán, Robin E. Harte (2006)

Studia Mathematica

Similarity:

Using axiomatic joint spectra we obtain a functional calculus which extends our previous Gelfand-Waelbroeck type results to include a Banach-valued Taylor-Waelbroeck spectrum.

The Słodkowski spectra and higher Shilov boundaries

Vladimír Müller (1993)

Studia Mathematica

Similarity:

We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.

On the axiomatic theory of spectrum

V. Kordula, V. Müller (1996)

Studia Mathematica

Similarity:

There are a number of spectra studied in the literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra, which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semiregular or essentially semiregular).

On a certain class of subspectra

Andrzej Sołtysiak (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.