arXiv subjects

Xiujuan Ma

Publications and source records attributed to Xiujuan Ma.

3 recordsLinked to original sources

arXiv2014

A note on unital full amalgamated free products of quasi-diagonal C*-algebras

In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite dimensional C*- algebra is quasidiagonal. Applying this result, we conclude that a unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree.

math.OA↗

arXiv2013

Local derivations on Rings containing a von Neumann algebra and a question of Kadison

We prove that if M is a von Neumann algebra whose abelian summand is discrete, then every local derivation on the algebra of all measurable operators affilated with M is a derivation. This answers a question of Richard Kadison.

math.OA↗

arXiv2007

On spectra and Brown's spectral measures of elements in free products of matrix algebras

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 $(M_2(\cc), {1/2}Tr)*(M_2(\cc), {1/2}Tr)$.

math.OA↗