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19th International Conference on Operator Theory
June 27 - July 2, 2002
Institute of Mathematics of the Romanian Academy and the Faculty of Mathematics of the West University of Timisoara
Timisoara, Romania

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Separate and joint similariry to families of (bounded) normal operators on Hilbert space
by
Piotrek Niemiec
Jagiellonian University

Sets of bounded linear operators S, T subset B(H) (H is a Hilbert space) are similar if there exists an invertible (in B(H)) operator G such that G-1·S·G=T. A bounded operator is scalar if it is similar to a normal operator. S is jointly scalar if there exists a set N subset B(H) of normal operators such that S and N are similar. S is separately scalar if every its element is scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented.

Continuous algebra homomorphisms between the algebra of all complex-valued continuous functions on a compact Hausdorff space and the algebra of all bounded operators in a Hilbert space are studied.

Date received: May 28, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiz-31.