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Results tagged with hilbert-spaces
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user 7311
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
4
votes
Accepted
"Frobenius-finite" linear operators on a Hilbert Space
Since $\sum_{(i,j)∈S×S}|a_{i ,j}|^2 =$ Trace$(A^*A)$ the answers to 1. and 2. are both affirmative, and as has already been said, the answer to 3. is "Hilbert-Schmidt."
- 15.3k
23
votes
Accepted
Monotone functions are differentiable a.e. and Hilbert's Fifth Problem: what's the connection?
Well, I cannot say for certain, but I did know Gleason well (he was my thesis advisor, and we wrote a paper together after that) and I have written an essay about Gleason's work on the Fifth Problem ( …
- 15.3k
4
votes
Can a self-adjoint operator have a continuous set of eigenvalues?
Recall that the spectrum of an operator $A$ on a Hilbert space is the set of vales $\lambda$ such that $A-\lambda I$ does not have a bounded inverse . So if $A$ is multiplication by a function in $L^2 …
- 15.3k