Displaying similar documents to “Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces”

Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces

P. Holický, O. F. K. Kalenda, L. Veselý, L. Zajíček (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. ...

On nested sequences of convex sets in Banach spaces

Jesús M. F. Castillo, Manuel González, Pier Luigi Papini (2014)

Studia Mathematica

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We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.

Paraconvex functions and paraconvex sets

Huynh Van Ngai, Jean-Paul Penot (2008)

Studia Mathematica

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We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded....