Analysis Seminar

Zack Cramer, University of Waterloo

“Matrix Algebras with a Certain Compression Property”

A subalgebra A of Mn(C) is said to be projection compressible if PAP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all idempotents E ∈ Mn(C). While it is immediate that every idempotent compressible algebra is also projection compressible, the converse is much less clear. Despite the fact that many preliminary examples can be shown either to exhibit the idempotent compression property or lack the projection compression property, a direct proof that these notions coincide remains remarkably elusive.

In this talk, we will classify the unital projection compressible subalgebras of Mn(C) up to transposition and unitary equivalence. As a result, we provide an answer to the question “Is every unital projection compressible subalgebra of Mn(C) in fact idempotent compressible?”

This is partially joint work with Laurent Marcoux and Heydar Radjavi.

MC 5417