Abstract
A projection P on a Banach space X is called "almost locally minimal" if, for every α > 0 small enough, the ball B(P, α) in the space L(X) of all operators on X contains no projection Q with ∥Q∥ ≤ ∥P∥(1 - Dα2) where D is a constant. A necessary and sufficient condition for P 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 ℓn1.
Original language | English |
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Pages (from-to) | 253-268 |
Number of pages | 16 |
Journal | Israel Journal of Mathematics |
Volume | 110 |
DOIs | |
State | Published - 1999 |