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Segal algebras, approximate identities and norm irregularity in C₀(X,A)

Jussi Mattas (2013)

Studia Mathematica

We study three closely related concepts in the context of the Banach algebra C₀(X,A). We show that, to a certain extent, Segal extensions, norm irregularity and the existence of approximate identities in C₀(X,A) can be deduced from the corresponding features of A and vice versa. Extensive use is made of the multiplier norm and the tensor product representation of C₀(X,A).

Seminorme submoltiplicative su algebre di funzioni

Nicola Rodino (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this note we study algebra seminorms on a functions algebra and we relate the existence of algebra norms on C ⁢ ( X ) with the topology of X . Also a theorem, that states which are the continuous characters, is demonstrated in a class of seminormed algebras.

Several characterizations for the special atom spaces with applications.

Geraldo Soares de Souza, Richard O'Neil, Gary Sampson (1986)

Revista Matemática Iberoamericana

The theory of functions plays an important role in harmonic analysis. Because of this, it turns out that some spaces of analytic functions have been studied extensively, such as Hp-spaces, Bergman spaces, etc. One of the major insights that has developed in the study of Hp-spaces is what we call the real atomic characterization of these spaces.

Shilov boundary for holomorphic functions on some classical Banach spaces

María D. Acosta, Mary Lilian Lourenço (2007)

Studia Mathematica

Let ∞ ( B X ) be the Banach space of all bounded and continuous functions on the closed unit ball B X of a complex Banach space X and holomorphic on the open unit ball, with sup norm, and let u ( B X ) be the subspace of ∞ ( B X ) of those functions which are uniformly continuous on B X . A subset B ⊂ B X is a boundary for ∞ ( B X ) if ∥ f ∥ = s u p x ∈ B | f ( x ) | for every f ∈ ∞ ( B X ) . We prove that for X = d(w,1) (the Lorentz sequence space) and X = C₁(H), the trace class operators, there is a minimal closed boundary for ∞ ( B X ) . On the other hand, for X = , the Schreier space,...

Simultaneous stabilization in A ℝ ( )

Raymond Mortini, Brett D. Wick (2009)

Studia Mathematica

We study the problem of simultaneous stabilization for the algebra A ℝ ( ) . Invertible pairs ( f j , g j ) , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that α f j + β g j is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since A ℝ ( ) has stable rank two, we are faced here with a different situation....

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.

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