I know that the space of the all bounded linear maps between two Banach spaces, denoted by $L(X,Y)$, has a relationship with the  projective tensor space of X and Y, 
$$({X \widehat\otimes_{\pi} Y})^* = L(X,Y^*).$$ 
Is there  any relationship between the space of all compacts operators between the two spaces, denoted by K(X,Y), and the projective tensor space of X and Y?


Thanks in advance.