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Nov
15
comment show that $f(z)+f(z^2)+\cdots + f(z^n)+\cdots$ converges locally uniformly to an analytic function in the unit disk.
Use Morera's theorem and the fact that local uniform convergence lets you interchange the limit and the integral on a closed contour.
Nov
13
comment Weak Convergence and Weak Topology
however, note that the converse is not true: if $x$ is in the weak-closure of $A$, then it is not true that there is a sequence $x_n \in A$ which converges to $x$ weakly.
Nov
13
suggested rejected edit on Unique representations of positive integers?
Nov
13
comment Unique representations of positive integers?
first of all, you need to clarify what you mean by a "representation".
Nov
13
comment Show that $a^m$ is in $H$ for every $a$ in $G$
If a group $G$ has order $n$, and $a \in G$, then what can you say about $a^n$?
Nov
11
comment show that Mn(R) is not commutative
@AmritanshuPrasad I'm curious, is there a way of making that precise? Is there a nice probability measure on $M_n$ for which the probability that two random matrices commute is zero?
Nov
8
comment spectrum of compact operators
it does not depend on pairwise distinct eigenvalues. Any eigenvalue will have only finite multiplicity (the dimension of its eigenspace is finite. ) Hence, any limit point of the sequence $\phi(k)$ will be a limit point of the spectrum of $M_\phi$.
Nov
8
answered spectrum of compact operators
Oct
11
comment A continuous nonconstant function has uncountable range
use the intermediate value theorem
Sep
22
answered Sequential Equivalence Implies Topological Equivalence
Sep
17
accepted “Almost” Hilbert spaces
Sep
16
revised Every Banach space is quotient of $\ell_1(I)$
added a tag - reference request
Sep
16
suggested approved edit on Every Banach space is quotient of $\ell_1(I)$
Sep
15
comment “Almost” Hilbert spaces
I meant isometry, not isomorphism.
Sep
15
asked “Almost” Hilbert spaces
Aug
26
answered The boundary of an open subset of $[0,1]$ containing all rationals in $(0,1)$
Aug
23
comment Hilbert subspaces of $B(\mathbb{R}^n)$
I was trying $B(\mathbb{R}^2)$. I haven't even been able to find two matrices which satisfy the parallelogram law and are not scalar multiples.
Aug
23
asked Hilbert subspaces of $B(\mathbb{R}^n)$
Aug
10
answered Hilbert Space: Weak Convergence implies Strong Convergence
Aug
6
answered When is the matrix $A^{\ast} A$ isometric?