Illinois Journal of Mathematics

Genus $n$ Banach spaces

P. G. Casazza and M. C. Lammers

Full-text: Open access

Abstract

We show that the classification problem for genus $n$ Banach spaces can be reduced to the unconditionally primary case and that the critical case there is $n=2$. It is further shown that a genus $n$ Banach space is unconditionally primary if and only if it contains a complemented subspace of genus $(n-1)$. We begin the process of classifying the genus 2 spaces by showing they have a strong decomposition property.

Article information

Source
Illinois J. Math., Volume 43, Issue 2 (1999), 307-323.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255985217

Digital Object Identifier
doi:10.1215/ijm/1255985217

Mathematical Reviews number (MathSciNet)
MR1703190

Zentralblatt MATH identifier
0943.46004

Subjects
Primary: 46B15: Summability and bases [See also 46A35]
Secondary: 46B07: Local theory of Banach spaces

Citation

Casazza, P. G.; Lammers, M. C. Genus $n$ Banach spaces. Illinois J. Math. 43 (1999), no. 2, 307--323. doi:10.1215/ijm/1255985217. https://projecteuclid.org/euclid.ijm/1255985217


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