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Nov
3
awarded  Enlightened
Nov
3
awarded  Nice Answer
Oct
31
awarded  Popular Question
Oct
29
comment Showing that $f$ continuous
@sammath I added an open set proof.
Oct
29
revised Showing that $f$ continuous
added 502 characters in body
Oct
29
comment Different norm on $\ell_p$-space and Hilbert space
I don't know the answer to your second comment but I'm interested in seeing answers in this thread here.
Oct
29
comment Different norm on $\ell_p$-space and Hilbert space
I'm not sure whether it will be a Hilbert space but I think it will. E.g. if you take the set of all $1.5$-summable sequences $c_n$ I see no reason why $\sum_n c_n \overline{c_n}$ would not define an inner product.
Oct
29
comment Different norm on $\ell_p$-space and Hilbert space
Using this answer here you know that if $p \le q$ you can always endow $\ell^p$ with the $q$ norm.
Oct
29
comment Different norm on $\ell_p$-space and Hilbert space
That's an interesting question.
Oct
29
comment An abelian Banach algebra without characters
I wonder if there are any "easy" examples, like $L^p$ spaces or continuous functions. Of course these are all non-examples but something "common" would be nice. Alas, I don't know any "common" algebra that has empty character space : (
Oct
28
awarded  Popular Question
Oct
27
revised Showing that $f$ continuous
added 667 characters in body
Oct
27
comment Showing that $f$ continuous
@sammath Regarding your edit: I will edit my answer accordingly.
Oct
27
comment Showing that $f$ continuous
@sammath I thought about it but I don't see how to do it. I'm sorry to not be of more help.
Oct
27
comment Function that is uniformly continuous but not bounded?
Wonderful. The shortest answers are the best answers.
Oct
27
answered Showing that $f$ continuous
Oct
26
comment Diagonalisable linear operator on infinite-dimensional vector space: definition problem
I think I have seen a definition for Hilbert spaces: If $e_n$ is an orthonormal basis for a Hilbert space $H$ then $T$ is diagonal if $Te_n = \lambda_n e_n$ for some $\lambda_n \in \mathbb C$. Not sure this helps.
Oct
26
comment Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
Related: math.stackexchange.com/questions/982355/…
Oct
26
comment If every subspace of V is T-invariant, prove that T is a multiple of the identity map.
Hello? I think your answer contains a few typos.
Oct
26
reviewed Approve Prove that minimal polynomial of $T =$ minimal polynomial of$ A$, if$ T(B) = AB$