Functor of a tensor product is a main tool of the study of the category of mo-dules in the Homological Algebra; On the basis of [1]

we have discussed the tensorproduct of B-spaces and got some results

in this paper.Let B-spaces E and {Ei

j∈J} be given

then E∪_(Ei()∪E()E_. If βand βi are cross-norm

then E(?)?∪i=1? E? is an isometry with a subspace of ∪i=1~(Eβj Ei). Next. we generalize Adjoint Isomorphism Theory of the HomologicalAlgebra. Let E1

E2 and F be B-spaces. then (B1_ E2

F)(E2

(E1

F)) and (E1(?)E2

F)(?)(E1

(?)(E2

F)). Finally

let Ei

F_ibe B-spaces

f∈(?)(E1

F1)

g∈(?)(E2

F2)

then exists uniquely f(?)g∈(?)(E1(?)E2

F1(?)β2 F2). Let P={sum from i to fi (?)gi}

then P is an isomotry with adense subspace of (?)(E1

F1)(?)?(?)(E2

F2). Specially

we identity E1 (?)E_2with a subspace of(E1(?)? E2). The sign on this paper is identified with [1]