Aug
15
comment Is Banach space a correct context to study sequences and series?
There are a lot of ways to generalize series. You can go beyond countable sums and consider uncountable series (though they are not so different); you can consider series with values in different algebraic structures (e. g. Banach spaces, lattices etc); you can construct continuous series aka integrals. There is so much room for generalization, that I consider thi squestion as too broad.
Aug
14
revised Convolution of $L^1(G)$ functions with elements of $M(G)$.
added 9 characters in body
Aug
14
comment A basic functional analysis doubt
No for details see this answer
Aug
13
revised $R\mbox{ is a right multiplier and }R(a)b=a\overset{?}{\implies} A\mbox{ is unital }$
edited tags
Aug
12
comment Convex Sets in Functional Analysis?
My first comment was helpful and reasonable. See two upvotes. Your next comment was "guess what I want to hear as answer" is stupid, therefore my tough second comment. And the last, if you came up with an answer, don't waste the time and efforts of other - just answer your question.
Aug
12
comment Convex Sets in Functional Analysis?
@bolbteppa I know that word, and it is a wrong answer.
Aug
11
comment Convex Sets in Functional Analysis?
Though it sounds offensive, I must say that since you ask such question you should close Bourbaki and read something more down-to-earth.
Aug
11
awarded Enlightened
Aug
10
comment When does an integral operator belong to the Schatten - von Neumann class in terms of its kernel?
I found that people consider very special cases of this problem, so general problem is unmanageabale
Aug
10
awarded Nice Answer
Aug
10
answered Let $X$ be a metric space with metric $d$. Show that $d:X \times X \longrightarrow \mathbb{R}$ is continuous.
Aug
10
comment When does an integral operator belong to the Schatten - von Neumann class in terms of its kernel?
Google integral operator, Shatten p-class
Aug
10
revised How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?
edited title
Aug
10
awarded Revival
Aug
10
revised Using Stone–Weierstrass theorem for completely regular space
added 2 characters in body
Aug
10
answered Proof that $(L^1)\neq(L^\infty)^\ast$
Aug
10
comment continuity in the strong topology implies continuity in the weak one
possible duplicate of Example of a net in $\mathcal{B}(\ell_2)$ that converges in the weak operator topology but not in the strong operator topology?
Aug
10
comment How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?
@barakmanos $$\frac{2}{\sqrt{4-3x+2x^2-x^3}}-1=x\implies 2=(x+1)\sqrt{4-3x+2x^2-x^3}\implies (4-3x+2x^2-x^3)(x+1)^2=4\implies x(x^4-5)=0$$
Aug
10
answered How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?
Aug
9
comment Show that $C^1([0,1])$ is not reflexive
Another method: in fact $X:=C^1([0,1])$ contains a copy of $c_0$, becuase $X\cong C([0,1])\oplus\mathbb{C}$ and $C([0,1])$ contains a copy of $c_0$. Hence if $X$ is reflexive, then so does $c_0$. Contradiction.
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