This is an announcement for the paper "A class of Banach spaces with
few non strictly singular operators" by S. A. Argyros, J. Lopez-Abad,
and S. Todorcevic.
Abstract: We construct a family $(\mathcal{X}_\al)_{\al\le \omega_1}$
of reflexive Banach spaces with long transfinite bases but with no
unconditional basic sequences. In our spaces $\mathcal{X}_\al$ every
bounded operator $T$ is split into its diagonal part $D_T$ and its
strictly singular part $S_T$.
Archive classification: Functional Analysis; Logic
Mathematics Subject Classification: 46B20; 03E05
Remarks: 52 pages, 1 figure
The source file(s), om1hi.tex: 252736 bytes, om1hi1.eps: 181035 bytes,
is(are) stored in gzipped form as 0312522.tar.gz with size 117kb. The
corresponding postcript file has gzipped size 325kb.
Submitted from: jlopez(a)crm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0312522
or
http://arXiv.org/abs/math.FA/0312522
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