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ArticleOriginal scientific text

Title

Additive combinations of special operators

Authors 1

Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan 30050, Republic of China

Abstract

This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible operators and cyclic operators. In each case, we are mainly concerned with the characterization of such combinations and the minimal number of the special operators required in them. We will omit the proofs of most of the results here but give some indication or brief sketch of the ideas behind and point out the remaining open problems.

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Banach Center Publications
1994/30/1
Export to PBN, Opens in new tab
Pages:
337-361
Main language of publication
English
Published
1994
Exact and natural sciences