Real hereditarily indecomposable Banach spaces and uniqueness of complex structure

Details Real hereditarily indecomposable Banach spaces and uniqueness of complex structure Real hereditarily indecomposable Banach spaces and uniqueness of complex structure

2005-11-07

arxiv.org/abs/math/0511166v2

Mathematics

Functional Analysis

32 pages

Scientific paper

There exists a real hereditarily indecomposable Banach space $X$ such that the quotient space $L(X)/S(X)$ by strictly singular operators is isomorphic to the complex field (resp. to the quaternionic division algebra). Up to isomorphism, the example with complex quotient space has exactly two complex structures, which are conjugate, totally incomparable, and both hereditarily indecomposable. So there exist two Banach spaces which are isometric as real spaces but totally incomparable as complex spaces. This extends results of J. Bourgain and S. Szarek from 1986. The quaternionic example, on the other hand, has unique complex structure up to isomorphism; there also exists a space with an unconditional basis, non isomorphic to $l_2$, which admits a unique complex structure. These two examples answer a question of Szarek.

Affiliated with

Also associated with

No associations

Rating

Real hereditarily indecomposable Banach spaces and uniqueness of complex structure does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Real hereditarily indecomposable Banach spaces and uniqueness of complex structure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Real hereditarily indecomposable Banach spaces and uniqueness of complex structure will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-336515