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Displaying 41 – 55 of 55

Rank and the Drazin inverse in Banach algebras

R. M. Brits, L. Lindeboom, H. Raubenheimer (2006)

Studia Mathematica

Let A be an arbitrary, unital and semisimple Banach algebra with nonzero socle. We investigate the relationship between the spectral rank (defined by B. Aupetit and H. Mouton) and the Drazin index for elements belonging to the socle of A. In particular, we show that the results for the finite-dimensional case can be extended to the (infinite-dimensional) socle of A.

Reciprocity theorems in the theory of representations of groups and algebras [Book]

Antoni Wawrzyńczyk (1975)

Representation of locally convex algebras.

L. Oubbi (1994)

Revista Matemática de la Universidad Complutense de Madrid

We deal with the representation of locally convex algebras. On one hand as subalgebras of some weighted space CV(X) and on the other hand, in the case of uniformly A-convex algebras, as inductive limits of Banach algebras. We also study some questions on the spectrum of a locally convex algebra.

Representation theory of locally $n$ -convex topological algebras

Anastasios Mallios (1972)

Mémoires de la Société Mathématique de France

Representations of tensor product L.M.C.*-Algebras 1.

Maria Fragoulopoulou (1983)

Manuscripta mathematica

Schur class operator functions and automorphisms of Hardy algebras.

Muhly, Paul S., Solel, Baruch (2008)

Documenta Mathematica

Schur Lemma and the Spectral Mapping Formula

Antoni Wawrzyńczyk (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Let B be a complex topological unital algebra. The left joint spectrum of a set S ⊂ B is defined by the formula $σ_{l} (S)$ = ${(λ (s))}_{s \in S} \in ℂ^{S} | {s - λ (s)}_{s \in S}$ generates a proper left ideal $.$ Using the Schur lemma and the Gelfand-Mazur theorem we prove that $σ_{l} (S)$ has the spectral mapping property for sets S of pairwise commuting elements if (i) B is an m-convex algebra with all maximal left ideals closed, or (ii) B is a locally convex Waelbroeck algebra. The right ideal version of this result is also valid.