On spectra and Brown's spectral measures of elements in free products of matrix algebras
| dc.creator | Fang, Junsheng | |
| dc.creator | Hadwin, Don | |
| dc.creator | Ma, Xiujuan | |
| dc.date | 2006-11-09 | |
| dc.date | 2007-07-28 | |
| dc.date.accessioned | 2026-07-07T08:20:35Z | |
| dc.date.available | 2026-07-07T08:20:35Z | |
| dc.description | We compute spectra and Brown measures of some non self-adjoint operators in $(M_2(\cc), {1/2}Tr)*(M_2(\cc), {1/2}Tr)$, the reduced free product von Neumann algebra of $M_2(\cc)$ with $M_2(\cc)$. Examples include $AB$ and $A+B$, where A and B are matrices in $(M_2(\cc), {1/2}Tr)*1$ and $1*(M_2(\cc), {1/2}Tr)$, respectively. We prove that AB is an R-diagonal operator (in the sense of Nica and Speicher \cite{N-S1}) if and only if Tr(A)=Tr(B)=0. We show that if X=AB or X=A+B and A,B are not scalar matrices, then the Brown measure of X is not concentrated on a single point. By a theorem of Haagerup and Schultz \cite{H-S1}, we obtain that if X=AB or X=A+B and $X\neq λ1$, then X has a nontrivial hyperinvariant subspace affiliated with $(M_2(\cc), {1/2}Tr)*(M_2(\cc), {1/2}Tr)$. | |
| dc.description | final version. to appear on Math. Scan | |
| dc.identifier | https://arxiv.org/abs/math/0611272 | |
| dc.identifier | http://arxiv.org/abs/math/0611272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135109 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54, 47C15 | |
| dc.title | On spectra and Brown's spectral measures of elements in free products of matrix algebras | |
| dc.type | text |