Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years...Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.展开更多
In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dime...In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dimensional closed subspace of X＊ if and only if X＊ contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.展开更多
文摘Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.
基金partially supported by NSFC,grant 11371296PhD Programs Foundation of MEC,Grant 20130121110032
文摘In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dimensional closed subspace of X＊ if and only if X＊ contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.
