A classification of projectors
Volume 67 / 2005
Banach Center Publications 67 (2005), 145-160
MSC: 47A64, 47A07, 46C99.
DOI: 10.4064/bc67-0-12
Abstract
A positive operator $A$ and a closed subspace $\cal S$ of a Hilbert space $\cal H$ are called compatible if there exists a projector $Q$ onto $\cal S$ such that $AQ=Q^*A$. Compatibility is shown to depend on the existence of certain decompositions of $\cal H$ and the ranges of $A$ and $A^{1/2}$. It also depends on a certain angle between $A({\cal S})$ and the orthogonal of $\cal S$.
