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Results tagged with fa.functional-analysis
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user 112001
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
6
votes
2
answers
474
views
Equivalence classes of norms on $R^n$ under symmetries
Let $G \leq {\bf GL}_n$ be a symmetry group on $\mathbb{R}^n$. For simplicity, we can consider the case $G = {\bf GL}_n$.
Define two norms $\|\cdot\|_1$ and $\| \cdot\|_2$ to be equivalent under $G$ …
- 252
1
vote
1
answer
671
views
Minimal value of matrix norm induced by a norm
Let $X$ be a finite dimensional Banach space and define a matrix norm $\| \cdot \|_{X}$ by
$$
\| A \|_{X} = \sup_{x \ne 0} \frac{\|A x\|_{X}}{\|x\|_{X}}
$$
where the matrix $A$ is interpreted as an …
- 252