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Results tagged with operator-norms
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user 16702
6
votes
1
answer
412
views
Absolutely 2-summable operator on a Hilbert space
An bouneded linear operator $A \in L(X, Y)$ (here $X$, $Y$ are Banach spaces) is called absolutely $2$-summable if there exists a $C>0$ such that
$$ \left( \sum_{j=1}^N \| A x_j\|_X^2 \right)^{1/2} \l …
- 9,853
2
votes
2
answers
320
views
Smooth dependence of the spectrum on the operator
I would like to know if there are theorems that state under which circumstances spectra of operator families depend smoothly on the parameter.
To clarify, suppose I have a 1-parameter family $T_h$ of …
- 9,853
3
votes
2
answers
3k
views
Weak convergence implies norm convergence for trace class operators?
It is known that weak convergence implies norm convergence in $\ell^1(\mathbb{N})$, see e.g. here.
Because of the typical analogies of the Schatten ideals $C_p \subset B(H)$ (where $H$ is a Hilbert s …
- 9,853