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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
0
votes
1
answer
267
views
Spectral Theorem, $AB = BA \implies B\Phi(f) = \Phi(f)B$
I'm studying the spectral theorem as appears in Reed and Simon's Functional Analysis.
Assume we have constructed the continuous functional calculus for a self adjoint bounded operator $A$ on a hilber …
2
votes
1
answer
154
views
Ergodic decomposition - how does restricting measure effect it? (Choquet Theory)
Suppose that $G$ is a discrete countable group and $\mu$ is an IRS (invariant random subgroup) of $G$: $\mu$ is conjugation invariant as a probability measure on the subgroups of $G$.
Since all the $ …