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M. Ganichev and N. J. Kalton
Convergence of the dual greedy algorithm in Banach spaces
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| Published: |
February 19, 2009 |
| Keywords: |
Dual greedy algorithm, convex functions, uniformly convex, uniformly smooth Banach spaces |
| Subject: |
41A65, 41A46, 46B20, 52A41 |
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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 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.
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| Acknowledgements
The authors were supported by NSF grant DMS-0244515 and DMS-0555670
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| Author information
M. Ganichev:
2335 Alexandria Pike, 63, Southgate, KY 41071
ganichev_m@yahoo.com
N. J. Kalton:
Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211
nigel@math.missouri.edu
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