# Counterexamples to a conjecture of Grothendieck

@article{Pisier1983CounterexamplesTA, title={Counterexamples to a conjecture of Grothendieck}, author={Gilles Pisier}, journal={Acta Mathematica}, year={1983}, volume={151}, pages={181-208} }

In his thesis ([7] II. p. 136) and in his fundamental paper ([6] p. 74), Grothendieck formulated the following conjecture: If two Banach spaces X and Y are such that their injective and projective tensor products X ~ Y and X ~ Y coincide, then either X or Y must be finite dimensional. The aim of this paper is to give a counterexample. We will exhibit a separable infinite dimensional Banach space X such that X~X=X~X, both algebraically and topologically. The space X is of cotype 2 as well as its…

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