Pseudo-Banach algebras
Quasicompact endomorphisms of commutative semiprime Banach algebras
This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if B is a unital commutative semisimple Banach algebra with connected character space, and T is a unital endomorphism of B, then T is quasicompact if and only if the operators Tⁿ converge in operator norm to a rank-one unital endomorphism of B. In this note the discussion is extended in two ways: we discuss endomorphisms of commutative...
Removing the interior of the spectrum
Ring homomorphisms on real Banach algebras.
Small deformations of topological algebras
We investigate stability of various classes of topological algebras and individual algebras under small deformations of multiplication.
Some algebras without submultiplicative norms or positive functionals
We prove a conjecture of Yood regarding the nonexistence of submultiplicative norms on the algebra C(T) of all continuous functions on a topological space T which admits an unbounded continuous function. We also exhibit a quotient of C(T) which does not admit a nonzero positive linear functional. Finally, it is shown that the algebra L(X) of all linear operators on an infinite-dimensional vector space X admits no nonzero submultiplicative seminorm.
Some remarks on derivations in Banach algebras and related results.
Some remarks on -algebras
We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that , are algebras and that is a -algebra if and only if .
Some Results about the Spectrum of Commutative Banach Algebras under the Weak Topology and Applications.
Stable elements of Banach and Fréchet algebras
We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.
Stable inverse-limit sequences, with application to Predict algebras
The notion of a stable inverse-limit sequence is introduced. It provides a sufficient (and, for sequences of abelian groups, necessary) condition for the preservation of exactness by the inverse-limit functor. Examples of stable sequences are provided through the abstract Mittag-Leffler theorem; the results are applied in the theory of Fréchet algebras.
Stable rank of Fourier algebras and an application to Korovkin theory.
Sur certaines questions concernant les Q-algèbres.
Sur la décomposition d'une algèbre topologique en produit cartésien d'idéaux
Sur la semi-norme spectrale supérieure en algèbre de Banach ultramétrique
Sur les conjectures de Hirschfeld et Zelazko dans les algèbres de Banach
Survey of some results in spectral theory obtained in Prague
The characteristic algebra of a polynomial covering map.
The compactum of a semi-simple commutative Banach algebra.
The group of invertible elements of a commutative Banach algebra