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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An extremely non-homogeneous weak Hilbert space


Authors: Spiros A. Argyros, Kevin Beanland and Theocharis Raikoftsalis
Journal: Trans. Amer. Math. Soc. 364 (2012), 4987-5014
MSC (2010): Primary 46B20, 46B06
Published electronically: April 6, 2012
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Abstract: We construct a weak Hilbert Banach space such that for every block subspace $ Y$ every bounded linear operator on $ Y$ is of the form $ D+S$, where $ S$ is a strictly singular operator and $ D$ is a diagonal operator. We show that this yields a weak Hilbert space whose block subspaces are not isomorphic to any of their proper subspaces.


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Additional Information

Spiros A. Argyros
Affiliation: Department of Mathematics, Zografou Campus, National Technical University, Athens 157 80, Greece
Email: sargyros@math.ntua.gr

Kevin Beanland
Affiliation: Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia 23284
Email: kbeanland@vcu.edu

Theocharis Raikoftsalis
Affiliation: Department of Mathematics, Zografou Campus, National Technical University, Athens 157 80, Greece
Email: th{\textunderscore}raik@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05592-9
PII: S 0002-9947(2012)05592-9
Keywords: Weak Hilbert spaces
Received by editor(s): February 7, 2011
Published electronically: April 6, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.