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Aug
11
comment induction exercise doubt
Hint: When do induction, you can not change the assumption, in your case, the assumption, $x_1x_2... x_{n+1}=1$ is the assumption, but you could translate your assumption into different form. Try set $x_i'=x_i for 1\leq i\leq n-1, x_n'=x_nx_{n+1}$.
Aug
11
comment What is the closed form for this sequence, powers of $4$?
try oeis.org, but it seems does not work...
Aug
11
comment Proof of Cauchy's Lemma in the case that G is abelian
Do reduction on order of $G$. As you did, take $U$, when $r>0$, focus on $U$, when $r=0$, consider $G/U$.
Aug
11
comment Existence of proper I.C.C. subgroup
Thanks for your quick answer, do you know any I.C.C. non amenable inner amenable groups satisfy this property?
Aug
11
accepted Existence of proper I.C.C. subgroup
Aug
11
comment Existence of proper I.C.C. subgroup
I do not understand why "g is contained in two separate cyclic subgroups". I think the following argument also works. Clearly, we can pick some $h_i$ with $h_i\not\in \langle g\rangle$ then $\langle h_i, g\rangle=T$ so $T$ is abelian, a contradition.
Aug
11
comment Compact operators on $L^2(G)$ as a reduced cross product of $C_0(G)$ and $G$.
Why $\mathbb{C}1 \otimes C^*(\pi(c_0(G)), \{\lambda_g : g \in G\}) \cong \mathcal{K}(\ell^2(G))$? And a first feeling is that $\lambda_g$ is not a compact operator.
Aug
11
asked Existence of proper I.C.C. subgroup
Aug
11
comment Almost everywhere measurable homomorphism
Could you give any reference for this result?
Jul
27
comment Why is the natural map from maximal to reduced C star algebra surjective?
I see, the second fact you mentioned is also used to show $||.||_{max}$ is the largest norm on algebraic tensor of two C star algebras, thanks a lot!
Jul
27
accepted Why is the natural map from maximal to reduced C star algebra surjective?
Jul
26
asked Why is the natural map from maximal to reduced C star algebra surjective?
Jul
21
accepted find element in relative commutant of a matrix subalgebra
Jul
19
comment find element in relative commutant of a matrix subalgebra
Thanks, I realized that the basic idea is to integral over the unitary group of $M_2(\mathbb{C})$ of $uau^{*}$, matrix units seems to play the role of unitary.
Jul
19
revised find element in relative commutant of a matrix subalgebra
fix typos
Jul
19
answered find element in relative commutant of a matrix subalgebra
Jul
19
asked find element in relative commutant of a matrix subalgebra
Jul
9
comment Short exact sequence involving mapping cone, cone, suspension of $C^*$-algebras
Do we have a natural morphism from SB to SA?
Jul
9
comment Maximal ideals and maximal subspaces of normed algebras
Natural examples of commutative unital non banach normed algebras are $RG$ for some commutative ring $R$ and abelian group $G$. For non-unital algebra, take any proper ideal of some algebra.
Jul
9
comment determing constant in inequality with nonnegative numbers
Something wrong in the second summand, there is only one term can appear in this notation