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Results tagged with fa.functional-analysis
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user 59219
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
7
votes
0
answers
473
views
Characterizing the sum $L^1 + L^\infty + L^{1,\infty} + L^{\infty, 1}$ of iterated Lebesgue ...
For the usual Lebesgue spaces $L^p (\mu)$ ($p \in [1,\infty]$) on a ($\sigma$-finite) measure space $(X,\mu)$, it is well-known that one has the characterization
$$
L^p (\mu) = \left\{f : X \to \Bbb{ …
- 734
5
votes
1
answer
374
views
Sufficient criteria for $X \subset \mathcal{H}$ to be a Lipschitz (or unif. cont.) retract o...
I am interested in sufficient criteria which ensure that a subset $X$ of a Hilbert space $\mathcal{H}$ is a Lipschitz (or at least uniformly continuous) retract of $\mathcal{H}$.
Under which condi …
- 734
1
vote
Accepted
Insights about a frame-like inequality
Yes, your starting inequality can only hold if $H$ has finite dimensional range. In fact, the dimension can be at most $q$.
To see this, let $Y$ denote the range of $H$. Your inequality implies (why? …
- 734