Matrix algebras with a certain compression property II

A subalgebra of Mn(C) is said to be idempotent compressible if EAE an algebra for all idempotents E∈Mn(C). Likewise, projection PAP orthogonal projections P∈Mn(C). In this paper, a case-by-case analysis used classify the unital subalgebras Mn(C), n≥4, up transposition and unitary equivalence. It observed that every shown admit compression property is, in fact, compressible. We therefore extend findings [3] setting M3(C), proving two notions compressibility agree matrix algebras.