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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
6
revised About $\infty$-norm on the space of convergent sequences
rolled back to a previous revision
Nov
6
revised About $\infty$-norm on the space of convergent sequences
added 1 character in body
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?
Nov
5
answered Counterexample to the set of all algebraic polynomials being dense in $[0,1]$
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