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Results tagged with fa.functional-analysis
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user 477204
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
5
votes
1
answer
201
views
Continuity of the extension of a tracial state with respect to the strong operator topology
Problem: Let $M\subseteq B(H)$ be a finite von Neumann algebra with a faithful tracial state $\tau$. Let $\widetilde{M}$ be the $\tau$-measurable operators on $M$ (recalled below). Extend the trace $\ …
- 85
3
votes
1
answer
217
views
$\tau$-measurable operator
Problem: Let $M$ be a semifinite von Neumann algebra with a faithful semifinite normal trace $\tau$. Let $m$ be a positive element in $M$ and let $e_{(0,\infty)}(m)$ be the spectral projection of $m$ …
- 85
2
votes
0
answers
119
views
Almost periodic functions in weak mixing extension
In Theorem 3.4.6 of the 'Lecture notes on ergodic theory' by Jesse Peterson, it is shown that in a weak mixing extension, every almost periodic function is trivial. I have a doubt in the proof of this …
- 85
1
vote
0
answers
349
views
Densely defined and closed operator
Question: Let $N\subseteq B(H)$ be a finite von Neumann algebra with a faithful normal trace $\tau$ and let $n\in N$. Let $B$ be a von Neumann subalgebra of $N$. Let $\mathbb{E}_B: N\rightarrow B$ be …
- 85