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Decomposable multipliers and applications to harmonic analysis

Kjeld Laursen, Michael Neumann (1992)

Studia Mathematica

For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves various closed...

Décomposition atomique des espaces de Bergman.

Frédéric Symesak (1995)

Publicacions Matemàtiques

The aim of this paper is to establish the theorem of atomic decomposition of weighted Bergman spaces Ap(Ω), where Ω is a domain of finite type in C2. We construct a kernel function H(z,w) which is a reproducing kernel for Ap(Ω) and we prove that the associated integral operator H is bounded in Lp(Ω).

Derivations into iterated duals of Banach algebras

H. Dales, F. Ghahramani, N. Grønbæek (1998)

Studia Mathematica

We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space A ( n ) is zero; i.e., ℋ 1 ( A , A ( n ) ) = 0 . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study...

Description of quotient algebras in function algebras containing continuous unbounded functions

Mati Abel, Jorma Arhippainen, Jukka Kauppi (2012)

Open Mathematics

Let X be a completely regular Hausdorff space, 𝔖 a cover of X, and C b ( X , 𝕂 ; 𝔖 ) the algebra of all 𝕂 -valued continuous functions on X which are bounded on every S ∈ 𝔖 . A description of quotient algebras of C b ( X , 𝕂 ; 𝔖 ) is given with respect to the topologies of uniform and strict convergence on the elements of 𝔖 .

Dirichlet series induced by the Riemann zeta-function

Jun-ichi Tanaka (2008)

Studia Mathematica

The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on ω , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form ( a p , s ) = ∏ p ( 1 - a p p - s ) - 1 for a p in ω . Among other things, using the Haar measure on ω for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.

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