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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 $\cal S$.

Authors

• Gustavo CorachDepartamento de Matemática
FI-UBA, and IAM-CONICET
Buenos Aires
Argentina
e-mail
• Alejandra MaestripieriInstituto de Ciencias, UNGS
San Miguel, Argentina
e-mail
• Demetrio StojanoffDepartamento de Matemática
FCE-UNLP
La Plata, Argentina
e-mail

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