Journal of Inequalities and Applications
Volume 6 (2000), Issue 3, Pages 247-251
Positive multiplication preserves dissipativity in commutative -algebras
Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, Padova 35131, Italy
Received 3 September 1999; Revised 29 September 1999
Copyright © 2000 Alvise Sommariva and Marco Vianello. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove that multiplication by a positive element preserves dissipativity (accretivity) in the framework of commutative -algebras. A simple counterexample shows that the result is not valid, in general, in commutative involutory Banach algebras.