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Small deformations of topological algebras

Mati Abel, Krzysztof Jarosz (2003)

Studia Mathematica

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

Michael Meyer (1995)

Studia Mathematica

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 Q -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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 ℓ p , ( 1 ≤ p ≤ ∞ ) are Q algebras and that A n = ℨ L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α > 1 / 2 .

Stable elements of Banach and Fréchet algebras

Graham Allan (1998)

Studia Mathematica

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

Graham Allan (1996)

Studia Mathematica

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.

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