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kent1251217291.pdf (213.11 KB)
ETD Abstract Container
Abstract Header
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES
Author Info
Sbeih, Reema
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291
Abstract Details
Year and Degree
2009, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
There is an extensive literature on linear maps and operators on Banach spaces. However, a corresponding non-linear theory is still in its beginning. We study non-linear maps between subsets of the classical Banach spaces and give estimates for the Banach-Mazur Lipschitz norm for some of the natural non-linear maps between unit spheres of these spaces. We show that the Banach-Mazur norm of these maps is much larger than the corresponding linear norms. We also study projections onto unit spheres of Banach spaces, we show that the scaling down projection is the best projection in
L
1
(0,1), and we give estimates for the
L
p
-spaces,
p
>1.
Committee
Per Enflo, PhD (Advisor)
Andrew Tonge, PhD (Committee Member)
Morley Davidson, PhD (Committee Member)
Kenneth Batcher, PhD (Committee Member)
Peter Tandy, PhD (Committee Member)
Pages
55 p.
Subject Headings
Mathematics
Keywords
d2
;
SCALING DOWN MAPS
;
ln
;
d1
;
b2
;
scaling down projection
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Citations
Sbeih, R. (2009).
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291
APA Style (7th edition)
Sbeih, Reema.
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES.
2009. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291.
MLA Style (8th edition)
Sbeih, Reema. "NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES." Doctoral dissertation, Kent State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291
Chicago Manual of Style (17th edition)
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Document number:
kent1251217291
Download Count:
625
Copyright Info
© 2009, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.