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A Minimal Invariant Set, Frames, and Operators

Beauvile, Robed (2024) A Minimal Invariant Set, Frames, and Operators. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In 1981, Dale Alspach produced the first example of a non-expansive mapping T on a weakly compact convex subset of a Banach space that is fixed point-free. Using Zorn’s lemma, there exists a minimally weak compact, convex subset of which is T-invariant and fixed point free. We will show that a special closed linear span contains a copy of the space of Lebesgue integrable function on the unit interval. Wenchang Sun introduced g-frames which are generalized frames and include ordinary frames. We will use many ideas from Operator Theory to show a characterization of Frames in terms of Riesz bases and a characterization of g-Frames in terms of g-Riesz bases.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Beauvile, Robedrobedbeauvil@gmail.comrob960009-0002-9733-4121
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLennard,
Committee MemberTurret,
Committee MemberDowling,
Committee MemberManfredi,
Committee MemberHajlasz,
Date: 10 January 2024
Date Type: Publication
Defense Date: 10 November 2023
Approval Date: 10 January 2024
Submission Date: 18 November 2023
Access Restriction: 2 year -- Restrict access to University of Pittsburgh for a period of 2 years.
Number of Pages: 126
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Frames, Generalized Frames, Fixed Point Theory
Date Deposited: 10 Jan 2024 13:39
Last Modified: 10 Jan 2024 13:39

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