Abstract of a paper by Valentin Ferenczi
This is an announcement for the paper "Real hereditarily indecomposable Banach spaces and uniqueness of complex structure" by Valentin Ferenczi. 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@ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0511166 or http://arXiv.org/abs/math.FA/0511166 or by email in unzipped form by transmitting an empty message with subject line uget 0511166 or in gzipped form by using subject line get 0511166 to: math@arXiv.org.
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Dale Alspach