Tuesday, 11 May 2010

Completely equivalent operator norms on -Banach algebras.

A priori, it does not make sense to talk about complete boundedness, since there are no specified operator space structure on A1 and A2.



In general, an infinite-dimensional Banach space can carry many incomparable operator space structure. Most prominently, there is the minimal and the maximal operator space structure (see Chapter 3 in the book of Gilles Pisier (see here). These two almost never the same.



There are criteria (also due to Pisier) which ensure that certain bounded maps between C-algebras are automatically completely bounded. This is related to the notion of length of a C-algebra. This is also explained in his book.

No comments:

Post a Comment