New answers tagged hilbert-spaces
2 votes
Accepted
Balls which are bounded weak neighborhoods of $0$
$\newcommand\de\delta$Yes, for $e\ne0$, the trivial lower bound $\|e\|+1$ can be improved (that is, replaced by a strictly smaller one) whenever the Banach space $E$ is $2$-smooth -- that is, $(2,D)$-...
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0 votes
From weak to norm continuity: uniqueness of representing measures on $C_b(H)$
$\newcommand\scT{\mathscr T}\newcommand\kp[1]{\kern.#1mm}\newcommand\rmd{\kern1.5mm{\rm d}\,}$In this answer, referring to the part "any insights or references would be greatly appreciated" ...
- 3,765
9 votes
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Question on functional calculus
The equality $\lVert f(A)\rVert=\lVert f\rVert_\infty$ is wrong for general Borel functions if $\lVert\cdot\rVert_\infty$ denotes the supremum norm on $\sigma(A)$ (this is why many books only state ...
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