Almost locally minimal projections in finite dimensional Banach spaces

A projectionP on a Banach spaceX is called “almost locally minimal” if, for every α>0 small enough, the ballB(P,α) in the spaceL(X) of all operators onX contains no projectionQ with whereD is a constant. A necessary and sufficient condition forP to be almost locally minimal is proved in the case of finite dimensional spaces. This criterion is used to describe almost locally minimal projections on ℓ ₁ ⁿ . Participant in Workshop in Linear Analysis and Probability, Texas A&M University, College Station, Texas, 1997. Partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany).