Date of Award

2010

Document Type

Dissertation/Thesis

Submission Date

October 2026

Abstract

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.

Comments

by Isaac DeFrain.

Extent

40 p.

Identifier

779183893

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