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Results tagged with fa.functional-analysis
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user 76115
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
6
votes
1
answer
2k
views
Comparing norms on tensor products of matrices
Given a Hilbert space $H$, let $S_1(H)$ denote the space of trace-class operators on $H$, with the trace-class norm or Schatten 1-norm. That is
$$ \Vert T \Vert_1 = \sum_{j\geq 1} |s_j| $$
where $(s_1 …
- 209
4
votes
1
answer
161
views
approximate diagonal
Let $I$ be an arbitary index set, $((A_i)_i,\|.\|_i)_{i\in I}$ be a family of Banach algebras, with approximate diagonal $(m^{i}_α)_α\subseteq A_i\hat\otimes A_i$, and $B=\{(x_i)_i\in {\displaystyle …
- 209
2
votes
2
answers
150
views
Approximately complemented subspaces
Definition:
Suppose $E$ is a subspace of normed space $X$. Then $E$ is approximately complemented in $X$ if for any compact subset $K$ of $E$ and any $\epsilon>0$ there is a continuous linear operator …
- 209