Classes of Invariant Subspaces for Some Operator Algebras

Hamhalter, Jan; Turilova, Ekaterina

doi:10.1007/s10773-013-1740-y

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Cited by 2 publications

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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%

Probability structures in subspace lattice approach to foundations of quantum theory

Turilova

2015

Lith Math J

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Noncommutative measure and probability theory develops parallel to classical probability theory. In our paper, we summarize recent results on the structure of subspaces affiliated with von Neumann algebras and noncommutative measures defined on them. We show the interplay of ideas from classical and noncommutative measure theories based on general inner product spaces and bring new examples in this area.MSC: 46L10, 46L51, 46S10

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