New York Journal of Mathematics
Volume 15 (2009) 73-95


M. Ganichev and N. J. Kalton

Convergence of the dual greedy algorithm in Banach spaces

Published: February 19, 2009
Keywords: Dual greedy algorithm, convex functions, uniformly convex, uniformly smooth Banach spaces
Subject: 41A65, 41A46, 46B20, 52A41

We show convergence of the weak dual greedy algorithm in wide class of Banach spaces, extending our previous result where it was shown to converge in subspaces of quotients of Lp (for 1<p<∞). In particular, we show it converges in the Schatten ideals Sp when 1<p<∞ and in any Banach lattice which is p-convex and q-concave with constants one, where 1<p<q<∞. We also discuss convergence of the algorithm for general convex functions.


The authors were supported by NSF grant DMS-0244515 and DMS-0555670

Author information

M. Ganichev:
2335 Alexandria Pike, 63, Southgate, KY 41071

N. J. Kalton:
Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211