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MathBS
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question
15
How to prove that there exist no functions $f,g:\Bbb{R}\to\Bbb{R}$ such that $f(g(x))=x^{2018}$ and $g(f(x))=x^{2019}$? [duplicate]
Jan 6, 2019
question
8
$(X,\mu)$ is a measure space. Show that, $L^\infty(X;\mu)$ is either finite dimensional or non-separable.
Nov 23, 2022
question
8
$f:[0,1]\to[0,1]$ be a continuous function. Let $x_1\in[0,1]$ and define $x_{n+1}={\sum_{i=1}^n f(x_i)\over n}$.Prove, $\{x_n\}$ is convergent
Jul 17, 2019
question
7
Let $S=\{AB-BA| A,B \in M_n(K)\}$ where $K$ is a field. Prove that $S$ is closed under matrix addition.
Nov 13, 2020
question
6
Let $A$ be a unital $C^*$-algebra, $a\in A,\ x,y\in A_{sa}$. Does there exist a state $\phi$ on $A$ such that $\phi(xa^*ay)=\lVert a\rVert^2\phi(xy)$?
Aug 1, 2023
question
6
Can a vector space over finite field be written as union of finite number of proper subspaces?
Nov 3, 2018
question
6
Condition when angle between two lines is ${\pi\over 3}$
Feb 27, 2019
question
5
Prove that $\lim_{n \to \infty} \frac{n}{(n!)^\frac{1}{n}} = e $ [duplicate]
Apr 30, 2018
question
5
Let $\alpha>0$. Show that $\sum_{n=1}^\infty {\sin nx\over n^\alpha}$ converges for all $x\in\Bbb{R}$ and examine continuity of the limit function.
Aug 7, 2020
question
5
Prove that, $\int_{0}^{2\pi}\frac{\cos x+2}{5+4\cos x} dx=\pi$
Feb 12, 2019