Tensor products of Tsirelson's space

Abstract

Tsirelson's space T has attracted considerable interest during the past few years, somewhat eclipsing the original space T* discovered in 1973 by B. S. Tsirelson [12]. However, in [1], the first two authors and Dineen showed that T* held the greater interest, from the point of view of holomorphic functions. Specifically, the main result of As a consequence, it is shown that the space (H(T*), "r,,,) of complex-valued holomorphic functions on T*, endowed with the Nachbin ported topology, is reflexive. Here, we continue our study of multilinear properties of T* by showing that P("T*) is "Tsirelson-like", in the sense that it is reflexive, with (not unconditional) basis, and contains no lr space for 1 <p < o0. In fact, our method of proof enables us to prove that (H(T*, 1,), .r,.,) and P("T*, 1,) are reflexive for all n 1,2,... and all p, 1 <p< o0.