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May
25
comment How to prove uniform continuity problem!
Okay, I'll try to add some stuff later (when I have time).
May
24
comment Rings having the same characters but not isomorphic.
I understand that $k[[t]]$ is probably the ring of formal power series but what is $k[[t]]t^{8 \nu}$?
May
24
comment Rings having the same characters but not isomorphic.
I'm sorry but I don't even understand the notation (I'm sure it's standard). Is $k$ a field and does $+$ denote direct sum?
May
22
comment If $g:V \rightarrow V$ is an injective linear transformation. Prove if $V$ is finite dimensional then $g$ is surjective.
Yes. That's the part I understand. Everything after "and so as..." is what I cannot follow.
May
22
comment If $g:V \rightarrow V$ is an injective linear transformation. Prove if $V$ is finite dimensional then $g$ is surjective.
I'm sorry but I don't understand your argument in $\implies$. It appears to me that you're using the rank nullity theorem in $\Longleftarrow$. And from your title I think it sounds that you're only aske to prove $\implies$.
May
15
comment Extending a functional with same norm
@MartinArgerami Thank you very much for your comment! For some reason I didn't get pinged and I only discovered it now by coincidence.
May
13
comment Reflexive normed spaces are Banach
@DanielFischer That's what I thought: nothing to prove at all.
May
13
comment Reflexive normed spaces are Banach
@DanielFischer But on Wikipedia condition (iii) would make $J$ an isomorphism of normed spaces...?
May
13
comment Reflexive normed spaces are Banach
@DanielFischer I don't think it's needed. It's enough that it's a normed vector space isomorphism, it doesn't need to be an isometry. Or am I missing something?
May
13
comment Extending a functional with same norm
@user23791 But you can. I'll add a second way of solving the question.
May
13
comment Extending a functional with same norm
@user23791 You don't need to construct it explicitly.
May
13
comment Extending a functional with same norm
@user23791 No, that's your sublinear map bounding $\phi_0$. Hahn-Banach doesn't construct an extension, it gives you its existence.
May
13
comment Extending a functional with same norm
I'm not clear what you're doing on line 2: the domain of $\phi_0$ is elements of the form $(2x,3x)$. How is $(0,2x)$ of this form? Is this a typo?
May
10
comment Best complex analysis references?
Here is a textbook that is freely available online: people.math.gatech.edu/~cain/winter99/complex.html
May
10
comment Is the linear operator $T_2^{-1}T_1 :U_1 \to U_2$ bounded if $T_1\in L(U_1,H)\ \ T_2 \in L(U_2,H)$ $\mathrm{ker}\ T_2=\{0\} $?
Nicely done. I got hung up on trying to find a counterexample. It seemed obvious that it should be enough to pick your favourite $T_1$ and any $T_2$ (with same image) such that $T_2^{-1}$ is discontinuous. And I'm still puzzled that that's not the case.
May
10
comment Is the linear operator $T_2^{-1}T_1 :U_1 \to U_2$ bounded if $T_1\in L(U_1,H)\ \ T_2 \in L(U_2,H)$ $\mathrm{ker}\ T_2=\{0\} $?
Linear but not necessarily continuous?
May
10
comment Is the linear operator $T_2^{-1}T_1 :U_1 \to U_2$ bounded if $T_1\in L(U_1,H)\ \ T_2 \in L(U_2,H)$ $\mathrm{ker}\ T_2=\{0\} $?
What is $L(\cdot,\cdot)$?
May
10
comment Best book for topology?
What book are we taking about? The link takes me to nowhere.
May
5
comment Proving a metric induces the product topology
@Dante You're absolutely right, I was a bit in a hurry when I wrote this. The $r/2$ is a typo, let me correct it (the claim is still true of course).
May
5
comment Continuity of the identity operator from weak to weak star topology
I will edit your title to add some more specific information about this question. Hope you don't mind.