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