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Alspach norm in classifying complemented subspaces of L[p], p > 2

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Date Issued:
2010
Summary:
Identifying and classifying the complemented subspaces of L p , p > 2, has provided much insight into the geometric structure of Lp . In 1981, Bourgain, Rosenthal, and Schechtman proved the existence of uncountably many isomorphically distinct complemented subspaces of L p , p > 2. In 1999, Dale Alspach introduced a systematic method of studying the complemented subspaces of Lp , p > 2. In this thesis, the theory of Lp spaces is developed with a concentration on techniques used to study the complemented subspaces. We define the Alspach norm and show that the possible complemented subspaces of Lp , p > 2, generated by two compatible partitions and weights are £2, £p, £2 EB £p, and(2.:EfJ £2)ep ' We have not discovered any previously unknown complemented subspaces of Lp , but this method has reduced the study and classification of these subspaces to a study of partitions of N.
Title: The Alspach norm in classifying complemented subspaces of L[p], p > 2.
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Name(s): DeFrain, Isaac.
Harriet L. Wilkes Honors College
Type of Resource: text
Genre: Thesis
Date Issued: 2010
Publisher: Florida Atlantic University
Physical Form: application/pdf
Extent: 40 p.
Language(s): English
Summary: Identifying and classifying the complemented subspaces of L p , p > 2, has provided much insight into the geometric structure of Lp . In 1981, Bourgain, Rosenthal, and Schechtman proved the existence of uncountably many isomorphically distinct complemented subspaces of L p , p > 2. In 1999, Dale Alspach introduced a systematic method of studying the complemented subspaces of Lp , p > 2. In this thesis, the theory of Lp spaces is developed with a concentration on techniques used to study the complemented subspaces. We define the Alspach norm and show that the possible complemented subspaces of Lp , p > 2, generated by two compatible partitions and weights are £2, £p, £2 EB £p, and(2.:EfJ £2)ep ' We have not discovered any previously unknown complemented subspaces of Lp , but this method has reduced the study and classification of these subspaces to a study of partitions of N.
Identifier: 779183893 (oclc), 3334256 (digitool), FADT3334256 (IID), fau:1395 (fedora)
Note(s): by Isaac DeFrain.
Thesis (B.A.)--Florida Atlantic University, Honors College, 2010.
Includes bibliography.
Subject(s): Alspach, Dale E. (Dale Edward), 1950-
Banach, Stefan, 1892-1945
L[p] spaces
Banach spaces
Multipliers (Mathematical analysis)
Functional analysis
Persistent Link to This Record: http://purl.flvc.org/FAU/3334256
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FADT3334256
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.

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