A positive operator A and a closed subspace of a Hilbert space ℋ are called compatible if there exists a projector Q onto such that AQ = Q*A. Compatibility is shown to depend on the existence of certain decompositions of ℋ and the ranges of A and . It also depends on a certain angle between A() and the orthogonal of .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-12, author = {Gustavo Corach and Alejandra Maestripieri and Demetrio Stojanoff}, title = {A classification of projectors}, journal = {Banach Center Publications}, volume = {68}, year = {2005}, pages = {145-160}, zbl = {1091.47017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-12} }
Gustavo Corach; Alejandra Maestripieri; Demetrio Stojanoff. A classification of projectors. Banach Center Publications, Tome 68 (2005) pp. 145-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-12/