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Hardy-type sequence spaces and Cesaro frames

Radelet, Dan (2009) Hardy-type sequence spaces and Cesaro frames. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Cesaro averaging is used in conjunction with Hardy space andHilbert space theory to realize certain types of convergence.In Chapter 1, we study certain Hardy-type sequence spaces, which are analogues ofell-infinity and c_0, respectively. We show that the Mazurproduct is not onto, which provides a new solution of Mazur's Problem 8 in the Scottish Book. We present corollaries for spaces defined via weighted ell-p seminorms and for c_0.In Chapter 2, we study the application of Cesaro operators onBessel sequences to realize a weak version of frame reconstructionin Hilbert space. Conditions for reconstruction via Markuschevichbases that are certain linear combinations of orthonormal basisvectors are given.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLennard, Chrislennard@pitt.eduLENNARD
Committee MemberBeatrous, Frankbeatrous@pitt.eduBEATROUS
Committee MemberDiestel,
Committee MemberDowling,
Committee MemberHeath, Robertrwheath@pitt.eduRWHEATH
Date: 30 September 2009
Date Type: Completion
Defense Date: 30 July 2009
Approval Date: 30 September 2009
Submission Date: 10 August 2009
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
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: Cesaro frame; Banach space; Hardy space; averaging; frame
Other ID:, etd-08102009-124755
Date Deposited: 10 Nov 2011 19:58
Last Modified: 15 Nov 2016 13:48


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