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

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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 ... continued below

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Schulle, Polly Jane August 2008.

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  • Schulle, Polly Jane

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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.

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  • August 2008

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  • May 11, 2009, 8:08 p.m.

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  • June 25, 2009, 1:59 p.m.

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Schulle, Polly Jane. Spaces of operators containing co and/or l ∞ with an application of vector measures., dissertation, August 2008; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc9036/: accessed December 11, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .