Property (H*) and Differentiability in Banach Spaces

PDF Version Also Available for Download.

Description

A continuous convex function on an open interval of the real line is differentiable everywhere except on a countable subset of its domain. There has been interest in the problem of characterizing those Banach spaces where the continuous functions exhibit similar differentiability properties. In this paper we show that if a Banach space E has property (H*) and B_E• is weak* sequentially compact, then E is an Asplund space. In the case where the space is weakly compactly generated, it is shown that property (H*) is equivalent for the space to admit an equivalent Frechet differentiable norm. Moreover, we define ... continued below

Physical Description

iii, 64 leaves

Creation Information

Obeid, Ossama A. August 1993.

Context

This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 19 times . More information about this dissertation can be viewed below.

Who

People and organizations associated with either the creation of this dissertation or its content.

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Obeid, Ossama A.

Provided By

UNT Libraries

With locations on the Denton campus of the University of North Texas and one in Dallas, UNT Libraries serves the school and the community by providing access to physical and online collections; The Portal to Texas History and UNT Digital Libraries; academic research, and much, much more.

Contact Us

What

Descriptive information to help identify this dissertation. Follow the links below to find similar items on the Digital Library.

Degree Information

Description

A continuous convex function on an open interval of the real line is differentiable everywhere except on a countable subset of its domain. There has been interest in the problem of characterizing those Banach spaces where the continuous functions exhibit similar differentiability properties. In this paper we show that if a Banach space E has property (H*) and B_E• is weak* sequentially compact, then E is an Asplund space. In the case where the space is weakly compactly generated, it is shown that property (H*) is equivalent for the space to admit an equivalent Frechet differentiable norm. Moreover, we define the SH* spaces, show that every SH* space is an Asplund space, and show that every weakly sequentially complete SH* space is reflexive. Also, we study the relation between property (H*) and the asymptotic norming property (ANP). By a slight modification of the ANP we define the ANP*, and show that if the dual of a Banach spaces has the ANP*-I then the space admits an equivalent Fréchet differentiability norm, and that the ANP*-II is equivalent to the space having property (H*) and the closed unit ball of the dual is weak* sequentially compact. Also, we show that in the dual of a weakly countably determined Banach space all the ANP-K'S are equivalent, and they are equivalent for the predual to have property (H*).

Physical Description

iii, 64 leaves

Subjects

Keywords

Library of Congress Subject Headings

Language

Identifier

Unique identifying numbers for this dissertation in the Digital Library or other systems.

Collections

This dissertation is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this dissertation?

When

Dates and time periods associated with this dissertation.

Creation Date

  • August 1993

Added to The UNT Digital Library

  • March 24, 2014, 8:07 p.m.

Description Last Updated

  • Jan. 29, 2015, 9:38 a.m.

Usage Statistics

When was this dissertation last used?

Yesterday: 0
Past 30 days: 1
Total Uses: 19

Interact With This Dissertation

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Obeid, Ossama A. Property (H*) and Differentiability in Banach Spaces, dissertation, August 1993; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc277852/: accessed September 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .