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Duality in Operator Spaces

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Abstract

It is well known that for any Hilbert space H the second dual of the space of all compact operators K(H) on H coincides with the space of all bounded operators L(H). In this note we generalize this statement to Banach spaces.

Partially supported by a grant from the National Science Foundation.

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References

  1. J. Diestel and J. J. Uhl Jr., Vector Measures, Amer. Math. Soc. Math. Surveys 15 (1977).

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  2. M. Feder and P. Saphar, Spaces of compact operators and their dual spaces, Israel J. Math. 21 (1975), 38–49.

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  3. G. Godefroy and P. Saphar, Duality in spaces of operators and smooth norms on Banach Spaces, Illinois J. of Math. 32 (1988), 672–695.

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  4. A. Pietsch, Operator Ideals, VEB, Deutscher Verlag der Wissenschaften, Berlin, 1978.

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© 1998 Springer-Verlag Berlin · Heidelberg

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Lomonosov, V. (1998). Duality in Operator Spaces. In: Abramovich, Y., Avgerinos, E., Yannelis, N.C. (eds) Functional Analysis and Economic Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72222-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-72222-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-72224-0

  • Online ISBN: 978-3-642-72222-6

  • eBook Packages: Springer Book Archive

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