We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T： H → Y so that （f ＋ T）-1 （NG（f-...We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T： H → Y so that （f ＋ T）-1 （NG（f-1）） is a r-null set of H, where NG（f-1） is the set of all the points of Gateaux non-diiTerentiability of f -1.展开更多
A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.Th...A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.展开更多
The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Fr...The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.展开更多
By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg n...By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.展开更多
基金supported by the National Natural Science Foundation of China(11171066)the Natural Science Foundation of Fujian Province(2013J01003)
文摘We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T： H → Y so that （f ＋ T）-1 （NG（f-1）） is a r-null set of H, where NG（f-1） is the set of all the points of Gateaux non-diiTerentiability of f -1.
基金Supported by the NSF of China (10071063 and 10471114)
文摘A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.
文摘The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.
文摘By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.
