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

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The State Space,.. Let . = U. . be a space satisfying condition II, and f be a positive ultraweakly continuous (relative to H . H) linear form defined on . such that m. = sup {f (B) ; 0 ≤ B ≤ A. B polynomial in A.} is finite for every i ≥ 0. Then, f has a unique positive ultraweakly continuous (relatively to . . .) extension to ..
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On Strong and Ultrastrong Topologies,The terms ‘σ-strong’, ‘strongest’, and ‘ultrastrong’ have the same meaning, and are used alternatively in the following treatment.
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Mathematical Physics Studieshttp://image.papertrans.cn/u/image/941050.jpg
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Technical Properties of the Domain,rhood V of zero such that, for every ɛ > 0, there exists a bounded set M. in E satisfying V ⊂ ɛU + M.. In particular, it is easily seen that every subspace A ⊂ B (., .) with A = A*, endowed with topology ρ, is quasi-normable.
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Gelfand Transformation,s (.,‖ ‖A..), i ∈ . are Banach spaces: it follows that . is an abelian ℂ *-algebra containing Id, and consists of operators sending D into itself. Let .’. be the Banach space dual of the ℂ* -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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