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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

2 votes
0 answers
494 views

Counterexample for closed graph theorem in unmetrizable case

Consider locally convex vector spaces $X,Y$ and let $A: X\to Y$ be a linear operator with closed graph. Closed Graph Theorem states that if $Y$ is Fréchet then $A$ is continuous. What is a counterexa …
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  • 465
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How general is the convergence of the exponential function's power series?

Suppose that $N$ is the set of all continuous semi-norms in $V$. For every semi-norm $p\in N$ there exists semi-norm $q \in N$ such that $p(\beta(a,b)) \leq q(a)q(b)$ --- this is a consequence of the …
Mikhail's user avatar
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