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 Jul 2 awarded Curious Feb 6 revised Possible restrictions on generators of $M_n(\mathbb{C})$ added 65 characters in body 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 added 11 characters in body 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 added 308 characters in body; added 14 characters in body; added 56 characters in body; added 32 characters in body May 31 awarded Supporter May 6 asked spectra of sums in (Banach) algebras