Compressible operators and the continuity of homomorphisms from algebras of operators
Volume 115 / 1995
Studia Mathematica 115 (1995), 251-259
DOI: 10.4064/sm-115-3-251-259
Abstract
The notion of a compressible operator on a Banach space, E, derives from automatic continuity arguments. It is related to the notion of a cartesian 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 operator on the James' space, J, is compressible, whence it follows that all homomorphisms from ℬ(J) are continuous.
