Banach ideals of operators with applications |
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Authors: | Y Gordon DR Lewis JR Retherford |
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Institution: | 1. Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803 USA;2. University of Florida, Gainesville, Florida 32601 USA |
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Abstract: | We present some results concerning the general theory of Banach ideals of operators and give several applications to Banach space theory. We give, in Section 3, new proofs of several recent results, as well as new operator characterizations of the p-spaces of Lindenstrauss and Pelczynski. In Section 4 we prove that the space of absolutely summing operators from E to F is reflexive if both E and F are reflexive and E has the approximation property. Section 5 concerns Hilbert spaces. In particular, we compute the relative projection constant of Hilbert spaces in Lp(μ)-spaces. |
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