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.
Citation
P. G. Casazza. M. C. Lammers. "Genus $n$ Banach spaces." Illinois J. Math. 43 (2) 307 - 323, Summer 1999. https://doi.org/10.1215/ijm/1255985217
Information
