Acta Mathematica

A hereditarily indecomposable $ {\mathcal{L}_{\infty}} $-space that solves the scalar-plus-compact problem

Spiros A. Argyros and Richard G. Haydon

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Abstract

We construct a hereditarily indecomposable Banach space with dual space isomorphic to 1. Every bounded linear operator on this space is expressible as λI + K, with λ a scalar and K compact.

Article information

Source
Acta Math., Volume 206, Number 1 (2011), 1-54.

Dates
Received: 25 March 2009
Revised: 5 February 2010
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892527

Digital Object Identifier
doi:10.1007/s11511-011-0058-y

Mathematical Reviews number (MathSciNet)
MR2784662

Zentralblatt MATH identifier
1223.46007

Subjects
Primary: 46B03: Isomorphic theory (including renorming) of Banach spaces
Secondary: 46B26: Nonseparable Banach spaces

Rights
2011 © Institut Mittag-Leffler

Citation

Argyros, Spiros A.; Haydon, Richard G. A hereditarily indecomposable $ {\mathcal{L}_{\infty}} $-space that solves the scalar-plus-compact problem. Acta Math. 206 (2011), no. 1, 1--54. doi:10.1007/s11511-011-0058-y. https://projecteuclid.org/euclid.acta/1485892527


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