2011
DOI: 10.1007/s10773-011-0665-6
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Subspace Structures in Inner Product Spaces and von Neumann Algebras

Abstract: We study subspaces of inner product spaces that are invariant with respect to a given von Neumann algebra. The interplay between order properties of the poset of affiliated subspaces and the structure of a von Neumann algebra is investigated. We extend results on nonexistence of measures on incomplete structures to invariant subspaces. Results on inner product spaces as well as on the structure of affiliated subspaces are reviewed.

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Cited by 3 publications
(1 citation statement)
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“…We would like to summarize and refine our recent results in this area, bring new illustrating examples, and outline problems for future research. This contribution has grown out of the papers [3,4,5,6,9,10,11,12,14,15,16]. For basic treatment on this field, the reader can consult also monographs [7,8].…”
Section: Introductionmentioning
confidence: 99%
“…We would like to summarize and refine our recent results in this area, bring new illustrating examples, and outline problems for future research. This contribution has grown out of the papers [3,4,5,6,9,10,11,12,14,15,16]. For basic treatment on this field, the reader can consult also monographs [7,8].…”
Section: Introductionmentioning
confidence: 99%