Generalized second-order derivatives of convex functions in reflexive Banach spaces
نویسندگان
چکیده
منابع مشابه
Second Order Differentiability of Convex Functions in Banach Spaces
We present a second order differentiability theory for convex functions on Banach spaces.
متن کاملUniformly convex Banach spaces are reflexive - constructively
We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the MilmanPettis theorem that uniformly convex Banach spaces are reflexive. Our aim in this note is to present a fully constructive analysis of the Milman-Pettis theorem [11, 12, 9, 13]: a uniformly convex Banach space is reflexive. First, t...
متن کاملOn the Second Derivatives of Convex Functions on Hilbert Spaces
Let be a proper l.s.c. convex function on a real Hilbert space H. We show that if H is separable, then 4> is twice differentiate in some sense on a dense subset of the graph of d.
متن کاملQ-reflexive Banach Spaces
Let E be a Banach space. There are several natural ways in which any polynomial P ∈ P(E) can be extended to P̃ ∈ P(E), in such a way that the extension mapping is continuous and linear (see, for example, [6]). Taking the double transpose of the extension mapping P → P̃ yields a linear, continuous mapping from P(E) into P(E). Further, since P(E) is a dual space, it follows that there is a natural ...
متن کاملOn Second Order Derivatives of Convex Functions on Infinite Dimensional Spaces with Measures
We consider convex functions on infinite dimensional spaces equipped with measures. Our main results give some estimates of the first and second derivatives of a convex function, where second derivatives are considered from two different points of view: as point functions and as measures.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1992
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1992-1088019-1