Reputation
2,408
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
Badges
10 27
Impact
~59k people reached

5h
comment Prove that all three metrics induces the same topology on $X_1\times X_2$
You can prove that this induces in each case the product topology.
1d
revised Composition involving bounded linear operators
added 31 characters in body
1d
comment Composition involving bounded linear operators
Ok, I see. Your operator $U$ is not linear and indeed my argument only works for Banach spaces.
1d
revised Composition involving bounded linear operators
deleted 81 characters in body
1d
answered Composition involving bounded linear operators
Feb
2
awarded  Notable Question
Jan
28
comment A set of $n$ vectors is a basis if and only if…
Probably the dimension of $V$ is fixed by $n$. Then a spanning set of $n$ vectors is linearly independent.
Jan
23
answered How to show path-connectedness of $GL(n,\mathbb{C})$
Jan
15
answered If $\int_0^1 f x^n dx=0, \forall n \in \mathbb{N} $, then $f\equiv 0.$
Jan
13
comment connected sets and ordered sets
Yes. The argument does not depend on the natural numbers.
Jan
9
awarded  Notable Question
Dec
27
awarded  Popular Question
Dec
23
comment Prob 3 Sec 9 in Munkres TOPOLOGY 2nd ed: injections $f_n\colon\{1,\ldots,n\}\to A$ implies an injection $f \colon\mathbb{N}\to A$?
I guess you need the axiom of (at least dependent) choice, to get $f$ since you define $f$ recursively. For the rest, the proof (and the idea) is right.
Dec
16
comment Positive logarithm in a $C^*$-algebra
Ok, thanks for confirmation.
Dec
16
accepted Positive logarithm in a $C^*$-algebra
Dec
14
comment Positive logarithm in a $C^*$-algebra
That is true, so I guess the exercise is just wrong ? See here for reference: books.google.de/…
Dec
14
revised Positive logarithm in a $C^*$-algebra
added 179 characters in body
Dec
14
revised Positive logarithm in a $C^*$-algebra
edited tags
Dec
14
comment Positive logarithm in a $C^*$-algebra
The questions is about the existence of some positive logarithm ... This is exercise 3.6 in Conways Book on Operator Theory.
Dec
14
asked Positive logarithm in a $C^*$-algebra