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Apr
22
answered What is the norm of the pre-multiplication by a fixed matrix operator?
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
Mar
27
comment inverse relation in a vector lattice
$\phi$ is not an operator, since $X_+$ is not a linear space
Mar
24
revised Analysis of the function $\prod\limits_{n=-\infty}^{ \infty }(1-e^{-a{(x+n)^2} })$
added 1 character in body; edited tags
Mar
24
comment Bijective bounded linear operator is invertible
This is not a step of the proof, this is an explanation why one had to keep in mind that $\ker A^*\neq\{0\}$.
Mar
24
revised Hamel basis and Banach spaces
edited body
Mar
24
answered Hamel basis and Banach spaces
Mar
24
answered Bijective bounded linear operator is invertible
Mar
24
comment Converse of uniform boundedness principle
A somewhat converse you may find in appendix D proposition 14 in Topics in Banach space theory. F. Albiac, N. Kalton
Mar
23
answered Does every LCS has a convex balanced local base?
Mar
22
comment Compact metric implies uncountable w*-dense set
(+1), nice and simple
Mar
21
comment Compact metric implies uncountable w*-dense set
you should ping Philip Brooker. He is a specialist on the subject of Szlenk index.
Mar
21
comment duality of $L^p$ spaces with non $\sigma$ finite measure
$(L_1)^*=L_\infty$ iff $\mu$ is localizable
Mar
19
awarded  Popular Question
Mar
17
awarded  Enlightened