Open Access
Fall 2012 Strictly singular operators in asymptotic $\ell_{p}$ Banach spaces
Anna Pelczar-Barwacz
Illinois J. Math. 56(3): 861-883 (Fall 2012). DOI: 10.1215/ijm/1391178553


We present a condition on higher order asymptotic behavior of basic sequences in a Banach space ensuring the existence of bounded noncompact strictly singular operators on a subspace. Applications concern asymptotic $\ell_{p}$ spaces, $1\leq p<\infty$, in particular convexified mixed Tsirelson spaces and related asymptotic $\ell_{p}$ HI spaces.


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Anna Pelczar-Barwacz. "Strictly singular operators in asymptotic $\ell_{p}$ Banach spaces." Illinois J. Math. 56 (3) 861 - 883, Fall 2012.


Published: Fall 2012
First available in Project Euclid: 31 January 2014

zbMATH: 1300.46009
MathSciNet: MR3161356
Digital Object Identifier: 10.1215/ijm/1391178553

Primary: 46B06 , 46B20

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 3 • Fall 2012
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