The Pettis Integral and Operator Theory

Thumbnail image of item number 1 in: 'The Pettis Integral and Operator Theory'.
Thumbnail image of item number 2 in: 'The Pettis Integral and Operator Theory'.
Thumbnail image of item number 3 in: 'The Pettis Integral and Operator Theory'.
Thumbnail image of item number 4 in: 'The Pettis Integral and Operator Theory'.
Showing 1-4 of 68 pages in this dissertation.

PDF Version Also Available for Download.

Use of this dissertation is restricted to the UNT Community. Off-campus users must log in to read.

Description

Let (Ω, Σ, µ) be a finite measure space and X, a Banach space with continuous dual X*. A scalarly measurable function f: Ω→X is Dunford integrable if for each x* X*, x*f L1(µ). Define the operator Tf. X* → L1(µ) by T(x*) = x*f. Then f is Pettis integrable if and only if this operator is weak*-to-weak continuous. This paper begins with an overview of this function. Work by Robert Huff and Gunnar Stefansson on the operator Tf motivates much of this paper. Conditions that make Tf weak*-to-weak continuous are generalized to weak*-to­weak continuous operators on dual spaces. For … continued below

Creation Information

Huettenmueller, Rhonda August 2001.

Context

This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by the UNT Libraries to the UNT Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 183 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.

Author

Chair

Committee Members

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Huettenmueller, Rhonda

Provided By

UNT Libraries

The UNT Libraries serve the university and community by providing access to physical and online collections, fostering information literacy, supporting academic research, and much, much more.

About | Browse this Partner

Contact Us

Corrections Questions

What

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

Degree Information

Description

Let (Ω, Σ, µ) be a finite measure space and X, a Banach space with continuous dual X*. A scalarly measurable function f: Ω→X is Dunford integrable if for each x* X*, x*f L1(µ). Define the operator Tf. X* → L1(µ) by T(x*) = x*f. Then f is Pettis integrable if and only if this operator is weak*-to-weak continuous. This paper begins with an overview of this function. Work by Robert Huff and Gunnar Stefansson on the operator Tf motivates much of this paper. Conditions that make Tf weak*-to-weak continuous are generalized to weak*-to­weak continuous operators on dual spaces. For instance, if Tf is weakly compact and if there exists a separable subspace D X such that for each x* X*, x*f = x*fχDµ-a.e, then f is Pettis integrable. This nation is generalized to bounded operators T: X* → Y. To say that T is determined by D means that if x*| D = 0, then T (x*) = 0. Determining subspaces are used to help prove certain facts about operators on dual spaces. Attention is given to finding determining subspaces far a given T: X* → Y. The kernel of T and the adjoint T* of T are used to construct determining subspaces for T. For example, if T*(Y*) ∩ X is weak* dense in T*(Y*), then T is determined by T*(Y*) ∩ X. Also if ker(T) is weak* closed in X*, then the annihilator of ker(T) (in X) is the unique minimal determining subspace for T.

Subjects

Keywords

Library of Congress Subject Headings

Language

Item Type

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.

About | Browse this Collection

What responsibilities do I have when using this dissertation?

Digital Files

When

Dates and time periods associated with this dissertation.

Creation Date

  • August 2001

Added to The UNT Digital Library

  • Sept. 25, 2007, 10:20 p.m.

Description Last Updated

  • May 13, 2013, 3:02 p.m.

Usage Statistics

When was this dissertation last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 183
More Statistics

Interact With This Dissertation

Here are some suggestions for what to do next.

Start Reading

Thumbnail image of item number 1 in: 'The Pettis Integral and Operator Theory'.
Thumbnail image of item number 2 in: 'The Pettis Integral and Operator Theory'.
Thumbnail image of item number 3 in: 'The Pettis Integral and Operator Theory'.
Thumbnail image of item number 4 in: 'The Pettis Integral and Operator Theory'.

PDF Version Also Available for Download.

Citations, Rights, Re-Use

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Links for Robots

Helpful links in machine-readable formats.

Archival Resource Key (ARK)

International Image Interoperability Framework (IIIF)

Metadata Formats

Images

URLs

Stats

Huettenmueller, Rhonda. The Pettis Integral and Operator Theory, dissertation, August 2001; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc2844/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .

Back to Top of Screen