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Jul
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awarded  Curious
Feb
6
revised Possible restrictions on generators of $M_n(\mathbb{C})$
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Feb
6
awarded  Commentator
Feb
6
asked Possible restrictions on generators of $M_n(\mathbb{C})$
Feb
6
comment Centralizer in a matrix algebra over commutative polynomials
Thank you. With this approach we are able to answer the question in affirmative.
Dec
19
asked Centralizer in a matrix algebra over commutative polynomials
Jan
10
comment Centralizers in C*-algebra
But it holds a+b=1, so b=f(a).
Jan
6
comment Centralizers in C*-algebra
I am interested in the situation of general $C^*$-algebras, and some "nontrivial" correspondence between $a$ and $b$. Since the correspondence in $B(H)$ is quite "strong", I expected that something nonobvious can be said also in general $C^*$-algebras.
Jan
5
comment Centralizers in C*-algebra
Since the condition trivially holds if A is commutative, we exclude that case. In the noncommutative case, does it hold the same correspondence as in $B(H)$?
Jan
4
comment Centralizers in C*-algebra
Yes, I am assuming that a and b are self-adjoint. Sorry for the mistake and thank you for pointing it out.
Jan
4
revised Centralizers in C*-algebra
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Jan
4
asked Centralizers in C*-algebra
Oct
30
comment positive hermitian elements in $M_n(\mathbb{C})$
I cannot find the question in Halmos books. There were some other useful information. Thank you. For case $n=2$, might Mathematica be able to compute this?
Oct
29
comment positive hermitian elements in $M_n(\mathbb{C})$
But $x^∗ax$ is also hermitian matrix if $a$ is. So $x^∗Px⊂P$, and $x^∗M_n(\mathbb{C})x=M_n(\mathbb{C})$ iff $x$ is invertible. So $x^∗Px$ either does not satisfy (iv) or equals $P$.
Oct
29
asked positive hermitian elements in $M_n(\mathbb{C})$
May
31
awarded  Editor
May
31
accepted spectra of sums in (Banach) algebras
May
31
revised spectra of sums in (Banach) algebras
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May
31
awarded  Supporter
May
6
asked spectra of sums in (Banach) algebras