Decomposability of finite rank operators in certain subspaces and algebras

Publisher： Cambridge University Press

E-ISSN： 1755-1633|64|2|307-314

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.64, Iss.2, 2001-10, pp. : 307-314

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

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 () be the set of all operators on H that annihilate all the operators of rank at most one in alg . We construct an atomic Boolean subspace lattice on H such that there is a finite rank operator T in () such that T does not have a rank one summand in (). We obtain some lattice-theoretic conditions on a subspace lattice which imply alg is strongly decomposable.

Related content

Additive maps preserving rank-one operators on nest algebras

By Bai Zhaofang  

Linear and Multilinear Algebra, Vol. 58, Iss. 3, 2010-04 ,pp. : 269-283 (15)

Taylor & Francis Ltd

Access to resources Recommend Favorite

Decomposability of free Łukasiewicz implication algebras

By Díaz Varela Jose  

Archive for Mathematical Logic, Vol. 45, Iss. 8, 2006-11 ,pp. : 1011-1020 (10)

Springer Publishing Company

Access to resources Recommend Favorite

Finite Rank Hankel Operators over the Complex Wiener Space

By Deck Thomas  

Potential Analysis, Vol. 22, Iss. 1, 2005-02 ,pp. : 85-100 (16)

Springer Publishing Company

Access to resources Recommend Favorite

Hyponormal Operators with Finite Rank Self-Commutators and Quadrature Domains

By Xia D.  

Journal of Mathematical Analysis and Applications, Vol. 203, Iss. 2, 1996-10 ,pp. : 540-559 (20)

Academic Press

Access to resources Recommend Favorite

Approximation of the rth differential operator by means of linear shape preserving operators of finite rank

By Sidorov S.P.  

Journal of Approximation Theory, Vol. 124, Iss. 2, 2003-10 ,pp. : 232-241 (10)

Elsevier

Access to resources Recommend Favorite