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