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Decomposability of finite rank operators in certain subspaces and algebras

Published online by Cambridge University Press:  17 April 2009

Jiankui Li
Jiankui Li
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, 410081, China Department of Mathematics, University of New Hampshire, Durham, NH 03824, United States of America, e-mail: [email protected]
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Let  be either a reflexive subspace or a bimodule of a reflexive algebra in B (H), the set of bounded operators on a Hilbert space H. We find some conditions such that a finite rank T ∈  has a rank one summand in  and  has strong decomposability. Let (ℒ) be the set of all operators on H that annihilate all the operators of rank at most one in alg ℒ. We construct an atomic Boolean subspace lattice ℒ on H such that there is a finite rank operator T in (ℒ) such that T does not have a rank one summand in (ℒ). We obtain some lattice-theoretic conditions on a subspace lattice ℒ which imply alg ℒ is strongly decomposable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 307 - 314
Copyright
Copyright © Australian Mathematical Society 2001

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