Vol. 40, No. 2, 1972

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On the operator M(Y ) = TY S1 in locally convex algebras

Florian Vasilescu

Vol. 40 (1972), No. 2, 489–500

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
Received: 11 May 1970
Published: 1 February 1972
Florian Vasilescu
Department of Mathematics
University of Lille 1
59655 Villeneuve d’Ascq