Standard weights on algebras of unbounded operators

Inoue, Atsushi; Karwowski, W.; Ogi, Hidekazu

doi:10.2969/jmsj/05140911

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Trace Representation Of Weights1

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2004

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“…Refer to [4,[13][14][15][16] for weights of O * -algebra and to [1,2,7,10] for partial O * -algebras. We put…”

Section: Trace Representation Of Weightsmentioning

confidence: 99%

Trace representation of weights on partial O∗-algebras

Inoue

Karwowski

Takakura

2004

Journal of Mathematical Analysis and Applications

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The purpose of this paper is to investigate when a weight ϕ on a partial O * -algebra M is a trace weighted by a positive self-adjoint operator Ω, that is, ϕ(X † 2 X) = tr(X † * Ω) * (X † * Ω) whenever X ∈ M s.t. X † ∈ L(X) and ϕ(X † 2 X) < ∞. It is shown that if M contains the inverse N of a positive compact operator such that the weak multiplication N 2 N is defined, then every weight ϕ on M + satisfying ϕ(N 2 N) < ∞ is a trace weighted by some positive trace operator.

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“…Refer to [4,[13][14][15][16] for weights of O * -algebra and to [1,2,7,10] for partial O * -algebras. We put…”

Section: Trace Representation Of Weightsmentioning

confidence: 99%