On the space \({\mathcal K}(P,P^*)\) of compact operators on Pisier space \(P\). (English) Zbl 0802.46015

John, Kamil

Note Mat. 12, 69-75 (1992).

Let \(P\) be a Pisier space, i.e. \(P \check\otimes P= P\widehat {\otimes} P\) and \(P\) and \(P^*\) are of cotype 2. The author first gives conditions such that all operators from \(P\) to \(P^*\) are compact and then constructs continuous projections on \({\mathcal L}(P, P^*)^*\) whose range is \({\mathcal K}(P, P^*)^*\) and whose kernel is the annihilator of \({\mathcal K}(P, P^*)\). In general, however, \({\mathcal K}(P, P^*)\) is not complemented in \({\mathcal L} (P, P^*)\).

Reviewer: H.König (Kiel)

MSC:

46A32	Spaces of linear operators; topological tensor products; approximation properties
47L05	Linear spaces of operators

Keywords:

tensor products; Pisier space; cotype 2; annihilator