Open Access
Summer 1999 Genus $n$ Banach spaces
P. G. Casazza, M. C. Lammers
Author Affiliations +
Illinois J. Math. 43(2): 307-323 (Summer 1999). DOI: 10.1215/ijm/1255985217


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.


Download Citation

P. G. Casazza. M. C. Lammers. "Genus $n$ Banach spaces." Illinois J. Math. 43 (2) 307 - 323, Summer 1999.


Published: Summer 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0943.46004
MathSciNet: MR1703190
Digital Object Identifier: 10.1215/ijm/1255985217

Primary: 46B15
Secondary: 46B07

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 2 • Summer 1999
Back to Top