COMPRESSIBLE OPERATORS AND THE CONTINUITY OF HOMOMORPHISMS FROM ALGEBRAS OF OPERATORS

The notion of a compressible operator on a Banach space, E, derives fr om automatic continuity arguments. It is related to the notion of a ca rtesian Banach space. The compressible operators on E form an ideal in B(E) and the automatic continuity proofs depend on showing that this ideal is large. In particular, it is shown that each weakly compact op erator on the James' space, J, is compressible, whence it follows that all homomorphisms from B(J) are continuous.