This is an announcement for the paper "A hereditarily indecomposable L_\infty-space that solves the scalar-plus-compact problem" by Spiros A Argyros and Richard G Haydon.

Abstract: We construct a hereditarily indecomposable Banach space with dual isomorphic to $\ell_1$. Every bounded linear operator on this space has the form $\lambda I+K$ with $\lambda$ a scalar and $K$ compact.

Archive classification: math.FA

Mathematics Subject Classification: 46B45

The source file(s), BD.tex: 14514 bytes Background.tex: 8660 bytes ConcRem.tex.bak: 13883 bytes Constr.tex: 14452 bytes HIDuals.tex: 12435 bytes Intro.tex: 3383 bytes Operators.tex: 9684 bytes RIS.tex: 22263 bytes ScalarPlusCompact.tex: 8259 bytes ellOneExact.tex: 15439 bytes, is(are) stored in gzipped form as 0903.3921.tar.gz with size 39kb. The corresponding postcript file has gzipped size 191kb.

Submitted from: richard.haydon@bnc.ox.ac.uk

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http://front.math.ucdavis.edu/0903.3921

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http://arXiv.org/abs/0903.3921

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