Standard reference:
$% Y. Raynaud, The range of a contractive projection in  L_p(H), Rev. Mat. Complut. 17 (2004), 485–512.%$

The Range of a Contractive Projection in L_p(H)

We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions is isometric to a -direct sum of Hilbert-valued -spaces. We explicit the structure of contractive projections. As a consequence for every the class of -direct sums of Hilbert-valued -spaces is axiomatizable (in the class of all Banach spaces).

Key words: contractive projections, vector-valued -spaces.
2000 Mathematics Subject Classification: Primary: 46B04, 46E40. Secondary: 46M07.