Journal of Inequalities and Applications 
Volume 6 (2000), Issue 3, Pages 247-251
doi:10.1155/S1025583401000145

Positive multiplication preserves dissipativity in commutative C∗-algebras

Alvise Sommariva and Marco Vianello

 Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, Padova 35131, Italy
Received 3 September 1999; Revised 29 September 1999

Abstract

We prove that multiplication by a positive element preserves dissipativity (accretivity) in the framework of commutative C∗-algebras. A simple counterexample shows that the result is not valid, in general, in commutative involutory Banach algebras.