Sinclair homomorphisms and semigroups of analytic functions
type: Item
instance of: scholarly article
title: Sinclair homomorphisms and semigroups of analytic functions
zbMATH Open document ID: 0882.46024
author: Thomas Vils Pedersen
published in: Journal of Functional Analysis
publication date: 1997-05-19T00:00:00Z
review text: The author studies homomorphisms from the convolution algebra \(L^1(\mathbb{R}^+)\) into certain Banach algebras of functions on the closed unit disc \(\mathbb{D}\). It is shown that for the algebra \(A^+\) of absolutely convergent Taylor series on \(\mathbb{D}\), every homomorphism \(\Phi\) is of the form \(\Phi(h)= \int^\infty_0 h(t)\nu^t dt\), \(\forall h\in L^1(\mathbb{R}^+)\), where \(\nu^t\) is a bounded, continuous semigroup in \(A^+\). A similar result holds for the algebra of functions analytic on the open disc and absolutely continuous on the unit circle. For the disc algebra and the Pisier algebra this is not true, but certain weaker representations are obtained.
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 43A20
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1011047
zbMATH Keywords: Sinclair homomorphisms
zbMATH Keywords: homomorphisms
zbMATH Keywords: convolution algebra
zbMATH Keywords: Banach algebras of functions on the closed unit disc
zbMATH Keywords: absolutely convergent Taylor series
zbMATH Keywords: algebra of functions analytic on the open disc and absolutely continuous on the unit circle
zbMATH Keywords: Pisier algebra
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: jfan.1996.3034
OpenAlex ID: W2006947463
cites work: Homogeneous algebras on the circle. I: Ideals of analytic functions
cites work: Q4741033
cites work: Q5618011
cites work: Q3320938
cites work: Q4758141
cites work: Q3244654
cites work: Q5727906
cites work: Q5590907
cites work: Q3215830
cites work: Q3687398
cites work: Q4197125
cites work: Random Fourier Series with Applications to Harmonic Analysis. (AM-101)
cites work: Some properties of the Pisier algebra
cites work: Norms of Powers in Banach Algebras
cites work: A remarkable homogeneous Banach algebra
cites work: One class of Toeplitz operators connected with the divisibility of analytic functions
cites work: Q3873013
cites work: Q3915472
cites work: Q3955918
cites work: A strong form of spectral synthesis
DOI: 10.1006/JFAN.1996.3034
description: scientific article; zbMATH DE number 1011047