# Additive combinations of special operators

Banach Center Publications (1994)

- Volume: 30, Issue: 1, page 337-361
- ISSN: 0137-6934

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topWu, Pei. "Additive combinations of special operators." Banach Center Publications 30.1 (1994): 337-361. <http://eudml.org/doc/262750>.

@article{Wu1994,

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.},

author = {Wu, Pei},

journal = {Banach Center Publications},

keywords = {additive combinations; sums; convex combinations; averages of operators; 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; cyclic operators},

language = {eng},

number = {1},

pages = {337-361},

title = {Additive combinations of special operators},

url = {http://eudml.org/doc/262750},

volume = {30},

year = {1994},

}

TY - JOUR

AU - Wu, Pei

TI - Additive combinations of special operators

JO - Banach Center Publications

PY - 1994

VL - 30

IS - 1

SP - 337

EP - 361

AB - 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.

LA - eng

KW - additive combinations; sums; convex combinations; averages of operators; 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; cyclic operators

UR - http://eudml.org/doc/262750

ER -

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