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

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