Projections in operator ranges
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- by Gustavo Corach, Alejandra Maestripieri and Demetrio Stojanoff PDF
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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.References
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 765-778
- MSC (2000): Primary 46C07, 47A62, 46C05
- DOI: https://doi.org/10.1090/S0002-9939-05-08007-X
- MathSciNet review: 2180895