Symmetric subspaces of l 1 with large projection constants

Bruce Chalmers; Grzegorz Lewicki

Studia Mathematica (1999)

  • Volume: 134, Issue: 2, page 119-133
  • ISSN: 0039-3223

Abstract

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We construct k-dimensional (k ≥ 3) subspaces V k of l 1 , with a very simple structure and with projection constant satisfying λ ( V k ) ≥ λ ( V k , l 1 ) > λ ( l 2 ( k ) ) .

How to cite

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Chalmers, Bruce, and Lewicki, Grzegorz. "Symmetric subspaces of $l_1$ with large projection constants." Studia Mathematica 134.2 (1999): 119-133. <http://eudml.org/doc/216626>.

@article{Chalmers1999,
abstract = {We construct k-dimensional (k ≥ 3) subspaces $V^k$ of $l_1$, with a very simple structure and with projection constant satisfying $λ(V^k) ≥ λ(V^k,l_1) > λ(l_2^\{(k)\})$.},
author = {Chalmers, Bruce, Lewicki, Grzegorz},
journal = {Studia Mathematica},
keywords = {relative and absolute projection constants},
language = {eng},
number = {2},
pages = {119-133},
title = {Symmetric subspaces of $l_1$ with large projection constants},
url = {http://eudml.org/doc/216626},
volume = {134},
year = {1999},
}

TY - JOUR
AU - Chalmers, Bruce
AU - Lewicki, Grzegorz
TI - Symmetric subspaces of $l_1$ with large projection constants
JO - Studia Mathematica
PY - 1999
VL - 134
IS - 2
SP - 119
EP - 133
AB - We construct k-dimensional (k ≥ 3) subspaces $V^k$ of $l_1$, with a very simple structure and with projection constant satisfying $λ(V^k) ≥ λ(V^k,l_1) > λ(l_2^{(k)})$.
LA - eng
KW - relative and absolute projection constants
UR - http://eudml.org/doc/216626
ER -

References

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  1. [CHFG] B. L. Chalmers, C. Franchetti and M. Giaquinta, On the self-length of two-dimensional Banach spaces, Bull. Austral. Math. Soc. 53 (1996), 101-107. Zbl0854.46012
  2. [CHM1] B. L. Chalmers and F. T. Metcalf, The determination of minimal projections and extensions in L 1 , Trans. Amer. Math. Soc. 329 (1992), 289-305. Zbl0753.41018
  3. [CHM2] B. L. Chalmers and F. T. Metcalf, A characterization and equations for minimal projections and extensions, J. Operator Theory 32 (1994), 31-46. Zbl0827.41016
  4. [CHPS] B. L. Chalmers, K. C. Pan and B. Shekhtman, When is the adjoint of a minimal projection also minimal, in: Approximation Theory (Memphis, Tenn., 1991), Lecture Notes in Pure and Appl. Math. 138, Dekker, 1992, 217-226. Zbl0761.41036
  5. [KS] M. I. Kadets and M. G. Snobar, Certain functionals on the Minkowski compactum, Mat. Zametki 10 (1971), 453-458 (in Russian); English transl.: Math. Notes 10 (1971), 694-696. Zbl0229.46018
  6. [HK] H. Koenig, Projections onto symmetric spaces, Quaestiones Math. 18 (1995), 199-220. 
  7. [PS] E. D. Positsel'skiĭ, Projection constants of symmetric spaces, Mat. Zametki 15 (1974), 719-727 (in Russian); English transl.: Math. Notes 15 (1974), 430-435. 
  8. [RU] D. Rutovitz, Some parameters associated with finite-dimensional Banach spaces, J. London Math. Soc. 40 (1965), 241-255. Zbl0125.06402
  9. [NT] N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Wiley, New York, 1989. Zbl0721.46004
  10. [WO] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, 1991. Zbl0724.46012

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