Relative entropy for maximal abelian subalgebras of matrices and the entropy of unistochastic matrices
| dc.creator | Choda, Marie | |
| dc.date | 2008-03-05 | |
| dc.date.accessioned | 2026-07-07T10:04:30Z | |
| dc.date.available | 2026-07-07T10:04:30Z | |
| dc.description | Let $A$ and $B$ be two maximal abelian *-subalgebras of the $n\times n$ complex matrices $M_n(\mathbb{C}).$ To study the movement of the inner automorphisms of $M_n(\mathbb{C}),$ we modify the Connes-St$ø$rmer relative entropy $H(A | B)$ and the Connes relative entropy $H_ϕ(A | B)$ with respect to a state $ϕ,$ and introduce the two kinds of the constant $h(A | B)$ and $h_ϕ(A | B).$ For the unistochastic matrix $b(u)$ defined by a unitary $u$ with $B = uAu^*,$ we show that $h(A | B)$ is the entropy $H(b(u))$ of $b(u).$ This is obtained by our computation of $h_ϕ(A | B).$ The $h(A | B)$ attains to the maximal value $\log n$ if and only if the pair $\{A, B\}$ is orthogonal in the sense of Popa. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0803.0591 | |
| dc.identifier | http://arxiv.org/abs/0803.0591 | |
| dc.identifier | Internat.J.Math.19(2008),767-776 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169701 | |
| dc.subject | Operator Algebras | |
| dc.subject | Mathematical Physics | |
| dc.title | Relative entropy for maximal abelian subalgebras of matrices and the entropy of unistochastic matrices | |
| dc.type | text |