The Action Constants

  • B. L. Chalmers
  • B. Shekhtman


In this paper we introduce isometric invariants of a given n-dimensional Banach space (cf [1]), conjecture (cf [1]) that these invariants characterize (up to isometry) the Banach space, and obtain several results and examples illustrating their usefulness. To start with, for a given space V, we look at the absolute projection constant and choose to view it as an extension constant of an identity operator on V.


Banach Space Space Versus Action Constant Converse Inequality Extension Constant 
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  1. 1.
    B. L. Chalmers and K. C. Pan, Finite-dimensional action constants, submitted.Google Scholar
  2. 2.
    B. L. Chalmers, K. C. Pan, and B. Shekhtman A strategy for proving extensions of the 4/3 conjecture, Proc. of Memphis Conf., Lect. Notes in Pure and Applied Math., 138 (1991), 207–215.MathSciNetGoogle Scholar
  3. 3.
    B. L. Chalmers and B. Shekhtman, Extension constants of unconditional two-dimensional operators, submitted.Google Scholar
  4. 4.
    B. L. Chalmers and B. Shekhtman, On the role of l in approximation theory, this volume.Google Scholar
  5. 5.
    N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-dimensional Operator Ideals, John Wiley and Sons, New York, 1989.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • B. L. Chalmers
    • 1
  • B. Shekhtman
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaRiversideUSA
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA

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