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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

10 votes
1 answer
2k views

Quantum functional analysis

Can one explain some philosophy behind "quantum functional analysis" (or "quantized functional analysis") which was initiated and developed by such researchers as: Ruan Z.-J., Pisier J., Effros E.G., …
8 votes

When is a Banach space a Hilbert space?

From the point of view of manifolds and curvature the following result is valid: A Banach space is a Hilbert space if and only if it is a NPC (non-positive curvature) space. http://www.iam.uni-bonn. …
Fedor Goncharov's user avatar
0 votes

Invertibility of an operator of the form $I-B$

I'm not sure if my unswer would be useful, but I have the following thing in mind. If B - is self-adjoint (symmetric) then it has a countable number of eigenvectors $e_j$ with eigenvalues which for …
Fedor Goncharov's user avatar
0 votes

L1 distance between gaussian measures

What you wrote is also a total variation distance between two Gaussian measures and $\sigma$ is calculated indeed via norm of Cameron-Martin space. I'm not sure what to do for example in the diagona …
Fedor Goncharov's user avatar
4 votes
0 answers
264 views

Concentration of infinite-dimensional Gaussian measure

I have the question about finding the subspace of concentration of a Gaussian Measure. More precisely: $\textbf{Question:}$ Assume we have a separable Hilbert space $\ell_2$ with Borel $\sigma$-algeb …