2d
comment Showing $r\in\mathbb Q\setminus \{0\}\implies e^r\notin \mathbb Q$
This is a standard trick it is used to prove irrationality of $\pi$, $\tan r$, $e^r$. One just needs to find a suitable integral. I learned that trick from this book
2d
answered Showing $r\in\mathbb Q\setminus \{0\}\implies e^r\notin \mathbb Q$
May
22
comment Is $B_{\ell_1}$ weak-metrizable?
Correct. $\phantom{}$
May
22
comment Is $B_{\ell_1}$ weak-metrizable?
$\ell_1^*=\ell_\infty$ but $\ell_\infty$ is not separable
May
18
comment Any injective *-homomorphism between finite dimensional C*-algebras is an isometry
This is well known that any injective involutive homomorphism between any C*-algebras is an isometry.
May
17
comment What algebraic structure do self-adjoint operators form?
It is a closed cone. Google positive cone of a C*-algebra
May
12
comment Convergence on Norm vector space.
Functional analysis is the study of linear spaces with additional structure
May
1
revised Show: Real roots of a polynomial
edited tags
Apr
28
revised Can $ {L^{1}}(G) $ be a $ C^{*} $-algebra?
deleted 1 character in body
Apr
27
answered Can $ {L^{1}}(G) $ be a $ C^{*} $-algebra?
Apr
22
answered What is the norm of the pre-multiplication by a fixed matrix operator?
Apr
22
awarded Excavator
Apr
22
awarded Editor
Apr
22
revised Equivalence between two automata
Broken link fixed
Apr
17
awarded Sportsmanship
Apr
5
comment how to show the derivative of the polynomial is bounded by itself in certain space.
The map $T:(\mathbb{C}_d[x], \Vert\cdot\Vert_\infty)\to (\mathbb{C}_d[x], \Vert\cdot\Vert_\infty):p\mapsto p'$ is continuous as any linear operator between finite dimensional spaces.
Apr
1
comment Properties maintained by the direct sum of normed spaces.
you should ask which properties you are interested, otherwise question is too broad
Mar
30
answered Infinite dimensional spaces other than functional spaces
Mar
28
revised Why dont we say if $f(U)$ is open for every open set $U$ in $A$, then $f$ is countinous?
edited tags; edited title
Mar
27
comment inverse relation in a vector lattice
$\phi$ may not be surjective, so $\phi^{-1}$ is not always well defined
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