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- W2035673251 abstract "Abstract The Banach spaces L ( X , Y ), K ( X , Y ), L w* ( X *, Y ), and K w* ( X *, Y ) are studied to determine when they contain the classical Banach spaces c o 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 c o or ℓ ∞ in K ( X , Y ) or L ( X , Y ). Results of Kalton, Feder, and Emmanuele concerning the complementation of K ( X , Y ) in L ( X , Y ) are generalized. Results concerning the complementation of the Banach space K w* ( X *, Y ) in L w* ( X *, Y ) are also explored as well as how that complementation affects the embedding of c o or ℓ ∞ in K w* ( X *, Y ) or L w* ( 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 c o . The paper contains a new result which classifies these spaces of operators. 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." @default.
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- W2035673251 date "2012-09-01" @default.
- W2035673251 modified "2023-09-27" @default.
- W2035673251 title "Non-complemented Spaces of Operators, Vector Measures, and co" @default.
- W2035673251 doi "https://doi.org/10.4153/cmb-2011-084-0" @default.
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