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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weak limits of projections and compactness of subspace lattices

Author: Bruce H. Wagner
Journal: Trans. Amer. Math. Soc. 304 (1987), 515-535
MSC: Primary 47D25
MathSciNet review: 911083
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Abstract: A strongly closed lattice of projections on a Hilbert space is compact if the associated algebra of operators has a weakly dense subset of compact operators. If the lattice is commutative, there are necessary and sufficient conditions for compactness, one in terms of the structure of the lattice, and the other in terms of a measure on the lattice. There are many examples of compact lattices, and two main types of examples of noncompact lattices. Compactness is also related to the study of weak limits of certain projections.

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Article copyright: © Copyright 1987 American Mathematical Society

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