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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Projections in operator ranges
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by Gustavo Corach, Alejandra Maestripieri and Demetrio Stojanoff PDF
Proc. Amer. Math. Soc. 134 (2006), 765-778 Request permission

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