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Results tagged with oa.operator-algebras
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user 4213
Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
6
votes
Representation of $*$-automorphism on finite dimensional matrix algebras
If $\phi$ is a $*$-automorphism then $\psi:A\mapsto\phi(\overline A)$
is a $\mathbb{C}$-automorphism. By the Skolem-Noether theorem
every $\mathbb{C}$-automorphism of $M_n(\mathbb{C})$ is inner,
that …
- 20.8k
25
votes
Commutative subalgebras of M_n
See the related question at
Dimension of subalgebras of a matrix algebra .
In particular, I'd recommend the reference:
M. Mirzakhani `A simple proof of a theorem of Schur'
Amer. Math. Monthly 105 (199 …
- 20.8k
5
votes
Commutative subalgebras of M_n
This is a reply to Tom's reply. Let's stick to commutative subalgebras
of $M_n(k)$ where $k$ is algebraically closed. Let $A$ be a unital
commutative subalgebra of $M_n(k)$. Then $N=k^n$ is a faithful …
- 20.8k
3
votes
Accepted
Intersection of ideals in C*-algebra or even rings in general
In the most general form, for arbitrary ideals over rings, this
is false. In the ring $\mathbb{Z}$ let $I_k$ be generated by $2^k$
and let $J$ be generated by $3$. Then $I_k+J=\mathbb{Z}$
for all $k$ …
- 20.8k