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Spaces of operators containing co and/or l ∞ with an application of vector measures.

The Banach spaces L(X, Y), K(X, Y), Lw*(X*, Y), and Kw*(X*, Y) are studied to determine when they contain the classical Banach spaces co or l ∞. The complementation of the Banach space K(X, Y) in L(X, Y) is discussed as well as what impact this complementation has on the embedding of co or l∞ in K(X, Y) or L(X, Y). Results concerning the complementation of the Banach space Kw*(X*, Y) in Lw*(X*, Y) are also explored and how that complementation affects the embedding of co or l ∞ in Kw*(X*, Y) or Lw*(X*, Y). The l p spaces for 1 ≤ p < ∞ are studied to determine when the space of compact operators from one l p space to another contains co. The paper contains a new result which classifies these spaces of operators. Results of Kalton, Feder, and Emmanuele concerning the complementation of K(X, Y) in L(X, Y) are generalized. A new result using vector measures is given to provide more efficient proofs of theorems by Kalton, Feder, Emmanuele, Emmanuele and John, and Bator and Lewis as well as a new proof of the fact that l ∞ is prime.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc9036
Date08 1900
CreatorsSchulle, Polly Jane
ContributorsBator, Elizabeth M., Lewis, Paul, Brozovic, Douglas
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsPublic, Copyright, Schulle, Polly Jane, Copyright is held by the author, unless otherwise noted. All rights reserved.

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