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Some Characterizations of Commutative Subspace Lattices
Author(s) -
Edwards D. A.
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002911
Subject(s) - mathematics , commutative property , hilbert space , separable space , subspace topology , bounded function , lattice (music) , mathematics subject classification , pure mathematics , bounded operator , norm (philosophy) , discrete mathematics , mathematical analysis , physics , political science , acoustics , law
Let H be a not necessarily separable Hilbert space, and let B H denote the space of all bounded linear operators on H . It is proved that a commutative lattice D of self‐adjoint projections in H that contains 0 and I is spatially complete if and only if it is a closed subset of B H in the strong operator topology. Some related results are obtained concerning commutative lattice‐ordered cones of self‐adjoint operators that contain D . 2000 Mathematics Subject Classification 47D03, 47L35, 47L07, 46L10, 54F05, 54G05, 46E05.