This is an announcement for the paper "Strictly singular uniform $\lambda-$adjustment in Banach spaces" by Boris Burshteyn.

Abstract: Based on the recently introduced uniform $\lambda-$adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and finitely strictly singular operators to the sequences of closed subspaces and operators in Banach spaces and prove theorems about lower semi--Fredholm stability. We also state some new open questions related to strict singularity and the geometry of Banach spaces.

Archive classification: math.FA

Mathematics Subject Classification: 32A70; 46A32; 46B50; 47A53; 47A55; 47B07

Remarks: 23 pages

The source file(s), boris997paper2.tex: 117155 bytes, is(are) stored in gzipped form as 0902.3045.gz with size 24kb. The corresponding postcript file has gzipped size .

Submitted from: boris997@astound.net

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0902.3045

or

http://arXiv.org/abs/0902.3045

or by email in unzipped form by transmitting an empty message with subject line

uget 0902.3045

or in gzipped form by using subject line

get 0902.3045

to: math@arXiv.org.