Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
Posted: September 28, 2005
MathSciNet review: 2180895
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Abstract | References | Similar Articles | Additional Information

Abstract: If $\mathcal{H}$ is a Hilbert space, 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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