[Banach] Abstract of a paper by Valentin Ferenczi
alspach at www.math.okstate.edu
Tue Nov 8 15:13:29 CST 2005
This is an announcement for the paper "Real hereditarily indecomposable
Banach spaces and uniqueness of complex structure" by Valentin
Abstract: 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; 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 examples answer a question of Szarek.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03; 46B04; 47B99
Remarks: 29 pages
The source file(s), cplexstructure_ferenczi.tex: 70811 bytes, is(are)
stored in gzipped form as 0511166.gz with size 22kb. The corresponding
postcript file has gzipped size 87kb.
Submitted from: ferenczi at ccr.jussieu.fr
The paper may be downloaded from the archive by web browser from
or by email in unzipped form by transmitting an empty message with
or in gzipped form by using subject line
to: math at arXiv.org.
More information about the Banach