Abstract :
LetX,Ybe two separable Banach spaces and letV⊂XandW⊂Ybe finite dimensional subspaces. Suppose thatV⊂S⊂X,W⊂Z⊂Yand letM∈L(S, V),N∈L(Z, W). We will prove that ifαis a reasonable, uniform crossnorm onX⊗YthenλM⊗N(V⊗αW,X⊗αY)=λM(V, X) λN(W, Y).Here for any Banach spaceX,V⊂S⊂XandM∈L(S, V)λM(V, X)=inf{‖P‖: P∈L(X, V),P |S=M}.Also some applications of the above mentioned result will be presented.
