 

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 


Abstract
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 L_{p} (for 1<p<∞). In particular, we show it converges
in the Schatten ideals S_{p} when 1<p<∞ and in any Banach lattice which is pconvex and qconcave with constants one, where 1<p<q<∞. We also discuss convergence of the algorithm for general convex functions.


Acknowledgements
The authors were supported by NSF grant DMS0244515 and DMS0555670


Author information
M. Ganichev:
2335 Alexandria Pike, 63, Southgate, KY 41071
ganichev_m@yahoo.com
N. J. Kalton:
Department of Mathematics, University of MissouriColumbia, Columbia, MO 65211
nigel@math.missouri.edu

