All Questions
Tagged with von-neumann-algebras weights
9 questions
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Takesaki II "Bimodule" question
Consider the following fragment from Takesaki's book "Theory of operator algebras", chapter IX Non-commutative integration, Section 3 on p187-188:
I have trouble understanding the equality
$...
- 175
2
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0
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121
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Invariant weights associated to algebraic quantum groups
Consider an algebraic quantum group $(A, \Delta)$ in the sense of Van Daele, i.e. a regular multiplier Hopf $^*$-algebra with a positive left integral $\varphi$ and a positive right integral $\psi$.
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2
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Tensor product of operator values weights (in the theory of locally compact quantum groups)
Let $M$ be a von Neumann algebra and $\psi$ a normal faithful semifinite weight on $M$. Then one should be able to form the object
$$\iota \otimes \psi: (M\overline{\otimes} M)_+ \to \widehat{M_+}.$$
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- 175
5
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2
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384
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Every locally compact group gives rise to a locally compact quantum group
A locally compact quantum group (in the sense of Vaes-Kustermans) consists of the data $(M, \Delta, \varphi, \psi)$ with $M$ a von Neumann algebra, $\Delta: M \to M \overline{\otimes} M$ a normal ...
- 175
3
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Takesaki: question about lemma in section "Left Hilbert algebras and weights"
To make this question relatively self-contained, this post is quite long, but the question itself is rather short.
Consider the following fragments in Takesaki's second volume "Theory of operator ...
- 175
2
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2
answers
481
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Takesaki II "Connes cocycle derivative"
Consider the following fragments from Takesaki's second volume "Theory of operator algebras" (chapter VIII $\oint 3$, Modular Automorphism groups, p107-108:
Why are the second and third ...
- 175
4
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1
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246
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Takesaki lemma 1.16 (volume II, chapter VII)
I am trying to understand the proof of the implication $(i)\implies (ii)$ in Takesaki's book "Theory of operator algebras II", chapter VII, which says the following:
The relevant setting ...
- 175
4
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2
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298
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Takesaki volume II chapter VII lemma 1.15
Consider the following fragments from Takesaki's second volume "Theory of operator algebras" in chapter VII on weight theory, lemma 1.15. Here $\mathcal{M}$ is a von Neumann algebra and $\...
- 175
2
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2
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158
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Decomposition of an element as a difference of positive elements in the definition subalgebra of a weight (Takesaki)
I originally asked this on MSE, but did not get an answer there.
Let $M$ be a von Neumann algebra. Let $\varphi: M_+ \to [0, \infty]$ be a weight on $M$. Consider
\begin{align*}&\mathfrak{p}_\...
- 175