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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Operator valued weighted sequence spaces
by
Novak Ivanovski
Department of Mathematics, University of Skopje
Coauthors: Marija Orovcanec (University of Skopje)

In this note we will give a generalization of weighted sequence spaces H2(\beta).

Definition. Let (Bn)\inftyn=0 be a sequence of positive invertible self-adjoint operators on a Hilbert space H with the property 0 < m < Bn < M,   for alln in N. We consider the space of vectors H2(B)={f=(f0, f1, ...): fi in H; \sumi=0\infty||Bifi||2 < \infty} with the inner product (f, g)B=\sumn=0\infty (Bnfn, Bngn).

The main results of this paper are as follows:

1. The space H2(B) is a Hilbert space.

2. Let (Bn)\inftyn=0 and (Cn)\inftyn=0 be sequences as in the the definition, then H2(B)=H2(C) and the norms are equivalent.

3. The unilateral shift U+ on H2(B) is unitarily equivalent to an invertible operator valued weighted shift on the space l2(H).

4. The operators U+ on H2(B) and H2(C) are similar.

5. We give a necessary and sufficient condition for the operators U+ on H2(B) and H2(C) to be unitarily equivalent.

1991 Mathematics Subject Classification 47B37.

(T)

Date received: April 13, 2000

Copyright © 2000 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 # caey-35.