The Range of a Contractive Projection in Lp(H)

  • Yves Raynaud
DOI: https://doi.org/10.5209/rev_REMA.2004.v17.n2.16763
Keywords: Contractive pro jections, Vector-valued Lp -spaces 2000 Mathematics Sub ject Classification, Primary, 46B04, 46E40 Secondary, 46M07

Abstract

We show that the range of a contractive pro jection on a Lebesgue-Bochner space of Hilbert valued functions Lp (H ) is isometric to a p -direct sum of Hilbert valued Lp -spaces. We explicit the structure of contractive pro jections. As a consequence for every 1 < p < the class Cp of p -direct sums of Hilbert valued Lp -spaces is axiomatizable (in the class of all Banach spaces).

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Published
2004-01-01
How to Cite
Raynaud Y. (2004). The Range of a Contractive Projection in Lp(H). Revista Matemática Complutense, 17(2), 485-512. https://doi.org/10.5209/rev_REMA.2004.v17.n2.16763
Issue
Vol. 17 No. 2 (2004)
Section
Articles

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