Titlebook: Unbounded Non-Commutative Integration; J. P. Jurzak Book 1985 D. Reidel Publishing Company, Dordretch, Holland 1985 Algebra.Topologie.calc

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-Invariance and ,-Traces,Neumann algebra (denoted always by P) generated by all A. and the center Z of M, we get a slightly different definition of .-invariance (with coincidence of both notions for a normal f . 0) and nothing is changed. Such a choice of P has to be taken in definition 9.2.

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實(shí)現(xiàn)

Technical Properties of the Domain,rhood V of zero such that, for every ? > 0, there exists a bounded set M. in E satisfying V ? ?U + M.. In particular, it is easily seen that every subspace A ? B (., .) with A = A*, endowed with topology ρ, is quasi-normable.

裝勇敢地做

Gelfand Transformation,s (.,‖ ‖A..), i ∈ . are Banach spaces: it follows that . is an abelian ? *-algebra containing Id, and consists of operators sending D into itself. Let .’. be the Banach space dual of the ?* -algebra . and K be the spectrum (i.e., the set of characters) of .’ which is known to be compact for σ (.’.,

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Cofinal Central Systems and Derivations, ā. (H) by hypothesis), such that the center of M. contains all ā.. Then it is clear that M. ? L (.), and it follows that . = U. M.A. × A. is a ?-algebra, with natural domain . satisfying condition I, with all A. as a cofinal central system.

標(biāo)準(zhǔn)

-Invariance and ,-Traces,be ultraweakly closed, satisfying condition II, with a cofinal sequence A., and let M be the von Neumann algebra .. We denote by P the abelian von Neumann algebra generated by all A. and by P. the group of unitary operators of P. Let . be the group of automorphisms of M of the form B ∈ M?U B U. ∈ M,

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