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Results tagged with fa.functional-analysis
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user 41105
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
1
answer
126
views
A sufficient condition for two semigroups to be norm equivalent?
Consider two densely defined, strictly positive, self-adjoint operators $A$ and $B$ with the following property
$$\|A^k x\| \simeq \|B^k x\|, \quad\forall x \in D(A^k)= D(B^k),$$
for $k=1,2,\cdots, M$ …
- 319
2
votes
1
answer
178
views
Estimate of semigroup with dual norm?
Consider a semigroup $(T(t))_{t\in\mathbb{R}^+}$ generated by a densely defined strictly positive symmetric linear operator $A: D(A) \subset X \to X$, where $X$ is a Banach space with norm $\|\cdot\|$ …
- 319
7
votes
2
answers
821
views
measurable linear functionals are also continuous on separable Banach spaces?
It is well known continuous linear functionals are (Borel) measurable. I have read, as a remark, the converse is also true for separable Banach spaces, but I could not find any references.
- 319