%0 Journal Article %1 fry2009approximation %A Fry, R. %A Keener, L. %D 2009 %K mathematics optimization %T Approximation of Lipschitz functions by Lipschitz, C^p smooth functions on weakly compactly generated Banach spaces %U http://arxiv.org/abs/0907.0241 %X This note corrects a gap and improves results in an earlier paper by the first named author. More precisely, it is shown that on weakly compactly generated Banach spaces X which admit a C^p smooth norm, one can uniformly approximate uniformly continuous functions f:X->R by Lipschitz, C^p smooth functions. Moreover, there is a constant C>1 so that any L-Lipschitz function f:X->R can be uniformly approximated by CL-Lipschitz, C^p smooth functions. This provides a `Lipschitz version' of the classical approximation results of Godefroy, Troyanski, Whitfield and Zizler.

@article{fry2009approximation, abstract = {This note corrects a gap and improves results in an earlier paper by the first named author. More precisely, it is shown that on weakly compactly generated Banach spaces X which admit a C^{p} smooth norm, one can uniformly approximate uniformly continuous functions f:X->R by Lipschitz, C^{p} smooth functions. Moreover, there is a constant C>1 so that any L-Lipschitz function f:X->R can be uniformly approximated by CL-Lipschitz, C^{p} smooth functions. This provides a `Lipschitz version' of the classical approximation results of Godefroy, Troyanski, Whitfield and Zizler.}, added-at = {2019-10-09T01:56:09.000+0200}, author = {Fry, R. and Keener, L.}, biburl = {https://www.bibsonomy.org/bibtex/2dd6b35549e0c6c3ff5f9b8aebfb27c19/kirk86}, description = {[0907.0241] Approximation of Lipschitz functions by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces}, interhash = {10b752c25b44b3bb0ce8a9b48c8f4714}, intrahash = {dd6b35549e0c6c3ff5f9b8aebfb27c19}, keywords = {mathematics optimization}, note = {cite arxiv:0907.0241Comment: Added comments, a few corrections. 16 pages}, timestamp = {2019-10-09T01:56:09.000+0200}, title = {Approximation of Lipschitz functions by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces}, url = {http://arxiv.org/abs/0907.0241}, year = 2009 }