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visits member for 4 years
seen 15 hours ago

Nov
24
comment Circle to circle homotopic to the constant map?
Ah, great, I understand. I think I can write the proof. Thank you very much for your comment!
Nov
23
comment Circle to circle homotopic to the constant map?
To get the extension do you apply some generalisation to $\mathbb R^2$ of Tietze's extension theorem?
Nov
18
comment Open and closed complex sets
Or one of the real parts was meant to be imaginary?
Nov
16
comment $\left\{\,f\in L^1[0,1]\,\big\vert\,\int_0^1\lvert f\rvert^2>1\right\}$ is open
Wouldn't it be easier to show that the closed unit ball is sequentially closed?
Nov
16
comment Does a continuous point-wise limit imply uniform convergence?
@IlmariKaronen Thank you for your comment! This is a great answer. I hope it gets some more upvotes.
Nov
16
comment Does a continuous point-wise limit imply uniform convergence?
Do I understand correctly: $f_n$ looks like a triangle getting smaller at the base? (piecewise linear function)
Nov
5
comment Counterexample to the set of all algebraic polynomials being dense in $[0,1]$
I see. So I guess an algebraic polynomial is the same as a polynomial. : )
Nov
5
comment Counterexample to the set of all algebraic polynomials being dense in $[0,1]$
What is an algebraic polynomial?
Oct
29
comment Showing that $f$ continuous
@sammath I added an open set proof.
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
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
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.