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Preservation of tensor sum and tensor product continuous functions

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Author(s): C. S. Kubrusly | N. Levan

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXX;
Issue: 1;
Start page: 133;
Date: 2011;
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Keywords: tensor product | tensor sum | Hilbert space operators

ABSTRACT
This note deals with preservation of tensor sum and tensor product of Hilbert space operators. Basic operations with tensor sum are presented. The main result addresses to the problem of transferring properties from a pair of operators to their tensor sum and to their tensor product. Sufficient conditions are given to ensure that properties preserved by ordinary sum and ordinary product are preserved by tensor sum and tensor product, which are equally relevant for both finite-dimensional and infinite-dimensional spaces.
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