NEW EXAMPLES OF NON-REFLEXIVE GROTHENDIECK SPACES

For Banach lattices E and X, let E (circle times) over cap (vertical bar pi vertical bar) X denote the Fremlin projective tensor product of E and X. It is shown that if 1 < p < infinity and X is both an AM -space with an order unit and a Grothendieck space, then l(p)(circle times) over cap (vertical bar pi vertical bar) X is a Grothendieck space. In particular, l(p)(circle times) over cap (vertical bar pi vertical bar) l(infinity), l(infinity)(circle times) over cap T-vertical bar pi vertical bar*, and, (circle times) over cap C-vertical bar pi vertical bar(K) are Grothendieck spaces, where T* is the original Tsirelson space and K is a compact stonean space, a compact sigma-stonean space, or a F-space.