2101.07666Jan 19, 202134 pages. Old project, already announced at several occasions in 2016, and that took a long time to be completed. Comments welcome v2: 37 pages. Section 5 added on the duality between Banach spaces and operators on full Lp spaces. A few references added
Given a set B of operators between subspaces of Lp spaces, we characterize the operators between subspaces of Lp spaces that remain bounded on the X
Nearby in the stack
-valued
Lp
space for every Banach space on which elements of the original class
B
are bounded. This is a form of the bipolar theorem for a duality between the class of Banach spaces and the class of operators between subspaces of
Lp
spaces, essentially introduced by Pisier. The methods we introduce allow us to recover also the other direction --characterizing the bipolar of a set of Banach spaces--, which had been obtained by Hernandez in 1983.