Vol. 40, No. 2, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On the operator M(Y ) = TY S1 in locally convex algebras

Florian Vasilescu

Vol. 40 (1972), No. 2, 489–500
Abstract

Let U be a locally convex separated unitary algebra over the complex field. If T and S are fixed elements of A and S is invertible, it is possible to define on A the linear operator

M  (Y ) = M (T,S)(Y) = TYS −1

for all Y A. The purpose of this paper is to construct a functional calculus with analytic functions for the operator M(T,S), by means of T and S, in order to obtain “multiplicative variants” of some results of M. Rosenblum. In the last section these results are applied to normal operators and matrices.

Mathematical Subject Classification 2000
Primary: 46H05
Secondary: 47A60
Milestones
Received: 11 May 1970
Published: 1 February 1972
Authors
Florian Vasilescu
Department of Mathematics
University of Lille 1
59655 Villeneuve d’Ascq
France