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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Projections in operator ranges


Authors: Gustavo Corach, Alejandra Maestripieri and Demetrio Stojanoff
Journal: Proc. Amer. Math. Soc. 134 (2006), 765-778
MSC (2000): Primary 46C07, 47A62, 46C05
Published electronically: September 28, 2005
MathSciNet review: 2180895
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Abstract: If $ \mathcal{H}$ is a Hilbert space, $ A$ is a positive bounded linear operator on $ \mathcal{H}$ and $ \mathcal{S}$ is a closed subspace of $ \mathcal{H}$, the relative position between $ \mathcal{S}$ and $ A^{-1}(\mathcal{S}^\perp)$ establishes a notion of compatibility. We show that the compatibility of $ (A,\mathcal{S})$ is equivalent to the existence of a convenient orthogonal projection in the operator range $ R(A^{1/2})$ with its canonical Hilbertian structure.


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Additional Information

Gustavo Corach
Affiliation: IAM-CONICET and Departamento de Matemática, FI-UBA, Paseo Colón 850, Buenos Aires (1063), Argentina
Email: gcorach@fi.uba.ar

Alejandra Maestripieri
Affiliation: IAM-CONICET and Instituto de Ciencias, UNGS, Los Polvorines, Argentina
Email: amaestri@ungs.edu.ar

Demetrio Stojanoff
Affiliation: IAM-CONICET and Departamento de Matemática, FCE-UNLP, La Plata, Argentina
Email: demetrio@ate.dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08007-X
PII: S 0002-9939(05)08007-X
Keywords: Oblique projections, operator ranges, positive operators
Received by editor(s): May 26, 2004
Received by editor(s) in revised form: October 14, 2004
Published electronically: September 28, 2005
Additional Notes: This work was partially supported by CONICET (PIP 2083/00), UBACYT I030 and ANPCYT (PICT03-9521)
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.