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Aug
25
awarded  Enlightened
Aug
25
awarded  Nice Answer
Aug
16
accepted When only eventually constant sequences are convergent?
Aug
16
comment When only eventually constant sequences are convergent?
Bad news, as always. Anyway thank you for these examples!
Aug
16
revised When only eventually constant sequences are convergent?
edited title
Aug
15
asked When only eventually constant sequences are convergent?
Aug
12
comment Random variables that span copies of $\ell_p$
All $\ell_p$ spaces except $\ell_1, \ell_2 and \ell_\infty$ are ad hoc constructions made by humans, not by God. Don't expect nice solutions here :)
Aug
9
answered Why's Daugavet equation important?
Aug
9
comment Is $\exists p\in\mathbb{N}:\frac{1}{\left| n^p \sin(n/2) \right|}$ is bounded for $n \in \mathbb{N}$?
Google irrationality measure of $\pi$
Jul
31
comment Infinite product of sine function
@PhoemueX this was a sloppy definition, now fixed
Jul
31
revised Infinite product of sine function
added 23 characters in body
Jul
31
reviewed Approve Infinite product of sine function
Jul
30
comment Evaluate $\displaystyle\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^\frac{1}{n} \ \mathrm{d}x$
Oh, I thought $\{\}$ parenthesis denoted fractional part here. Otherwise ignore first hint and immediately apple the second and the third ones.
Jul
30
comment Evaluate $\displaystyle\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^\frac{1}{n} \ \mathrm{d}x$
1 Fractional part is redundant here. 2 Apply dominated convergence theorem 3 Note that $\lim_{n\to\infty}(a^n+b^n)^{1/n}=\max(a,b)$ for positive $a$ and $b$.
Jul
30
revised $\ell^p$ as a direct summand of $L^p$
added 102 characters in body
Jul
30
answered $\ell^p$ as a direct summand of $L^p$
Jul
25
comment The space of continuous functions as a dual space
@AlexM.exactly.
Jul
25
comment The space of continuous functions as a dual space
@AlexM. As for your question in comments it is completely different. In fact the space of continuous functionals on $X^*$ endowed with weak* topology is exactly $X$. It is remains to note that for $X=C(K)$ we have $X^*=M(K)$.
Jul
25
comment The space of continuous functions as a dual space
Do you mean isometric isomorphism or arbitrary isomorphism of Banach spaces?
Jul
24
comment How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
Because you can put $n=n_k$ in the inequality $\Vert x_n-x_{n_k}\Vert<2^{-k}$.