Tensor products of maximal abelian subalgebras of C*-algebras
| dc.creator | Wassermann, Simon | |
| dc.date | 2007-11-01 | |
| dc.date | 2007-11-27 | |
| dc.date.accessioned | 2026-07-07T08:44:47Z | |
| dc.date.available | 2026-07-07T08:44:47Z | |
| dc.description | It is shown that if $C_1$ and $C_2$ are maximal abelian self-adjoint subalgebras (masas) of C*-algebras $A_1$ and $A_2$, respectively, then the completion $C_1\otimes C_2$ of the algebraic tensor product $C_1\odot C_2$ of $C_1$ and $C_2$ in any C*-tensor product $A_1\otimes_β A_2$ is maximal abelian provided that $C_1$ has the extension property of Kadison and Singer and $C_2$ contains an approximate identity for $A_2$. An example is given to show that $C_1\otimes C_2$ can fail to be a masa in $A_1\otimes_β A_2$ with $A_1$ and $A_2$ unital if neither $C_1$ nor $C_2$ has the extension property. This gives an answer to a long-standing question, but leaves open some other interesting problems, one of which turns out to have a potentially intriguing implication for the Kadison-Singer extension problem. | |
| dc.description | 10 pages. Revision 1. Simplifications in the examples in section 3, original first paragraph of section 4 deleted | |
| dc.identifier | https://arxiv.org/abs/0711.0131 | |
| dc.identifier | http://arxiv.org/abs/0711.0131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142783 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L06 | |
| dc.title | Tensor products of maximal abelian subalgebras of C*-algebras | |
| dc.type | text |