Harmonic calculus in involutive \(p\)-Banach algebras and applications
type: Item
instance of: scholarly article
title: Harmonic calculus in involutive \(p\)-Banach algebras and applications
zbMATH Open document ID: 1041.46031
author: Aziz Ifzarne
author: A. El Kinani
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2001-01-01T00:00:00Z
review text: Let \(A\) be a complex \(p\)-Banach algebra with \(0<p\leq 1\) which is endowed with a conjugate-linear involution \(*\). If \(a\in A\), then the authors define \(f(a)\) for any harmonic function \(f\) on a simply connected domain containing the spectrum of \(a\) by \(f(a)= g(a)+ h(a)^*\), where \(g\) and \(h\) are holomorphic functions such that \(f= g+ \overline h\). A number of features (including uniqueness, continuity, and a spectral mapping theorem) and applications (such as a square root lemma and analogues of the K. Fan and J. von Neumann inequalities) are shown.
reviewed by: Armando R. Villena
Mathematics Subject Classification ID: 46H30
zbMATH DE Number: 1931531
zbMATH Keywords: harmonic functional calculus
zbMATH Keywords: involutive \(p\)-Banach algebra
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1931531