[Banach] Abstract of a paper by Valentin Ferenczi

[Dale Alspach]

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 at ccr.jussieu.fr

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 http://front.math.ucdavis.edu/math.FA/0511166

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 http://arXiv.org/abs/math.FA/0511166

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