In this very valuable paper for given two linear spaces and we consider the space , the projective tensor product , and the injective tensor product . If and are Banach spaces then in we may introduce e.g. the projective crossnorm and the injective crossnorms . The main results of this paper are the following theorems:
(1) the space can be identified with the space (p. 383),
(2) the space can be identified with the space (p. 385); the same holds true for vector-valued functions,
(3) the space is identified with the space (p. 387);
(4) is isometrically isomorphic to the completion of the space (p. 389).
Very interesting and valuable are comments and remarks connected with the theorem of Grothendieck (p. 392) and the theorem of Littlewood-Orlicz-Grothendieck (p. 393).