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Results tagged with fa.functional-analysis
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user 58211
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
1
answer
147
views
Restriction of derivations on $C^\infty(X)$
In 'Kriegl, Michor - A convenient setting for global infintite-dimensional analysis', they say that for an element $x$ in a convenient (i.e. Mackey-complete locally convex) space $X$, a bounded deriva …
- 1,527
1
vote
1
answer
293
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Relation between locally convex calculus and Kriegl & Michor's "convenient setting"
I have a very general question regarding the book "Kriegl, Michor: The Convenient Setting of Global Analysis.":
Is the differential calculus of locally convex spaces (see here, for instance) canonical …
- 1,527
3
votes
0
answers
221
views
Non-compact analogue of Peter-Weyl
I have the following situation: $G$ is a real unimodular locally compact semisimple Lie group. Then it is known that the regular representation $H:=L^2(G,\mu_H)$ decomposes as
\begin{equation}
\int^{\ …
- 1,527
1
vote
0
answers
112
views
Projective tensor product continuous?
For $V$, $W$ Banach spaces, is the canonical morphism $B(V) \times_\pi B(W) \to B(V \hat{\otimes}_\pi W)$ continuous, where $B(V)$ denotes the set of all linear bounded endomorphisms with operator nor …
- 1,527
4
votes
1
answer
305
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Relation between dual of nuclear space $(\substack{\text{lim} \\ \leftarrow i} H_i)'$ and $\...
Let $\substack{\text{lim} \\ \leftarrow i} H_i$ be a nuclear space, considered as the limit of the codirected diagram $$... \to H_2 \to H_1 \to H_0,$$
with $f_{ji}:H_i \to H_j$ being the trace class …
- 1,527