A classification of projectors

G. CORACH, A. MAESTRIPIERI Y D. STOJANOFF

Polish Academy of Sciences, Warszawa.

Congreso; Topological algebras, their applications, and related topics. K. Jarosz and A. Soltysiak, Eds.; 2005

Polish Academy of Sciences

A positive operator $A$ and a closed subspace $cS$ of a Hilbert space $cH$ are called compatible  if thereexists a projector $Q$ onto $cS$ such that $AQ=Q^*A$.Compatibility is shown to depend on the existence ofcertain decompositions of H and the ranges of $A$ and$A^{1/2}$. It also depends on certain angle between $A(cS)$and the orthogonal of $cS$.