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Relations between some constants associated with finite dimensional Banach spaces

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Abstract

We define the asymmetry constants(E) of a Banach spaceE, and show examples of finite-dimensional spaces with “large” asymmetry constants. IfE isn-dimensional,λ(E)17its projection constant and π 1(I E ) the absolutely summing norm of the identity operatorI E , thenn≦λ(E)π1(I E )≤n(s(E))2. Similar equations linking thep-absolutely summing and the nuclear norms ofI E are established. We also obtain estimates on these norms, for example π2(I E )=√n.

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Authors and Affiliations

  1. St. John’s College, Cambridge, Lehigh University, Bethlehem, Pennsylvania

    D. J. H. Garling & Y. Gordon

  2. The Hebrew University of Jerusalem, Israel

    D. J. H. Garling & Y. Gordon

Authors
  1. D. J. H. Garling
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  2. Y. Gordon
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Additional information

The contribution of this author is a part of a Ph.D. Thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor J. Lindenstrauss whose guidance and valuable suggestions are gratefully acknowledged.

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Garling, D.J.H., Gordon, Y. Relations between some constants associated with finite dimensional Banach spaces. Israel J. Math. 9, 346–361 (1971). https://doi.org/10.1007/BF02771685

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  • DOI: https://doi.org/10.1007/BF02771685

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