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Power boundedness in Banach algebras associated with locally compact groups

E. Kaniuth, A. T. Lau, A. Ülger (2014)

Studia Mathematica

Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. Pursuing our investigations of power bounded elements in B(G), we study the extension property for power bounded elements and discuss the structure of closed sets in the coset ring of G which appear as 1-sets of power bounded elements. We also show that L¹-algebras of noncompact motion groups and of noncompact IN-groups with polynomial growth do not share the so-called power boundedness property. Finally, we give a characterization...

Products of n open subsets in the space of continuous functions on [0,1]

Ehrhard Behrends (2011)

Studia Mathematica

Let O₁,...,Oₙ be open sets in C[0,1], the space of real-valued continuous functions on [0,1]. The product O₁ ⋯ Oₙ will in general not be open, and in order to understand when this can happen we study the following problem: given f₁,..., fₙ ∈ C[0,1], when is it true that f₁ ⋯ fₙ lies in the interior of B ε ( f ₁ ) ⋯ B ε ( f ₙ ) for all ε > 0 ? ( B ε denotes the closed ball with radius ε and centre f.) The main result of this paper is a characterization in terms of the walk t ↦ γ(t): = (f₁(t),..., fₙ(t)) in ℝⁿ. It has to...

Proper uniform algebras are flat

R. C. Smith (2009)

Czechoslovak Mathematical Journal

In this brief note, we see that if A is a proper uniform algebra on a compact Hausdorff space X , then A is flat.

Properties of function algebras in terms of their orthogonal measures

Jan Čerych (1994)

Commentationes Mathematicae Universitatis Carolinae

In the present note, we characterize the pervasive, analytic, integrity domain and the antisymmetric function algebras respectively, defined on a compact Hausdorff space X , in terms of their orthogonal measures on X .

Quasicompact endomorphisms of commutative semiprime Banach algebras

Joel F. Feinstein, Herbert Kamowitz (2010)

Banach Center Publications

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...

Real linear isometries between function algebras. II

Osamu Hatori, Takeshi Miura (2013)

Open Mathematics

We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

Real-linear isometries between certain subspaces of continuous functions

Arya Jamshidi, Fereshteh Sady (2013)

Open Mathematics

In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin...

Real-linear isometries between function algebras

Takeshi Miura (2011)

Open Mathematics

Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → z ∈ ℂ: |z| = 1, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and T f = κ f o φ ¯ on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily...

Representations of the direct product of matrix algebras

Daniele Guido, Lars Tuset (2001)

Fundamenta Mathematicae

Suppose B is a unital algebra which is an algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X (Theorem 2.6). Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described (Theorem 3.3).

Representing measures for the disc algebra and for the ball algebra

Raymond Brummelhuis, Jan Wiegerinck (1991)

Annales Polonici Mathematici

We consider the set of representing measures at 0 for the disc and the ball algebra. The structure of the extreme elements of these sets is investigated. We give particular attention to representing measures for the 2-ball algebra which arise by lifting representing measures for the disc algebra.

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.

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