Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers; Grzegorz Lewicki

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 2, page 119-134
  • ISSN: 0066-2216

Abstract

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) ≤ λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ₂ ( 2 ) ) ≥ λ ( V ) for any two-dimensional real symmetric space V.

How to cite

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Chalmers, Bruce, and Lewicki, Grzegorz. "Two-dimensional real symmetric spaces with maximal projection constant." Annales Polonici Mathematici 73.2 (2000): 119-134. <http://eudml.org/doc/262661>.

@article{Chalmers2000,
abstract = {Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that $λ(V) ≤ λ(V_n)$ where $V_n$ is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that $4/π = λ(l₂^\{(2)\}) ≥ λ(V)$ for any two-dimensional real symmetric space V.},
author = {Chalmers, Bruce, Lewicki, Grzegorz},
journal = {Annales Polonici Mathematici},
keywords = {absolute projection constant; minimal projection; symmetric spaces},
language = {eng},
number = {2},
pages = {119-134},
title = {Two-dimensional real symmetric spaces with maximal projection constant},
url = {http://eudml.org/doc/262661},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Chalmers, Bruce
AU - Lewicki, Grzegorz
TI - Two-dimensional real symmetric spaces with maximal projection constant
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 2
SP - 119
EP - 134
AB - Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that $λ(V) ≤ λ(V_n)$ where $V_n$ is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that $4/π = λ(l₂^{(2)}) ≥ λ(V)$ for any two-dimensional real symmetric space V.
LA - eng
KW - absolute projection constant; minimal projection; symmetric spaces
UR - http://eudml.org/doc/262661
ER -

References

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  1. [1] 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. [2] B. L. Chalmers and F. T. Metcalf, The determination of minimal projections and extensions in L¹, Trans. Amer. Math. Soc. 329 (1992), 289-305. Zbl0753.41018
  3. [3] 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. [4] B. L. Chalmers and F. T. Metcalf, A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces, Ann. Polon. Math. 56 (1992), 303-309. Zbl0808.46016
  5. [5] H. Koenig, Projections onto symmetric spaces, Quaestiones Math. 18 (1995), 199-220. Zbl0827.46005
  6. [6] J. Lindenstrauss, On the extension of operators with a finite-dimensional range, Illinois J. Math. 8 (1964), 488-499. Zbl0132.09803
  7. [7] N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Wiley, New York, 1989. 
  8. [8] D. Yost, L₁ contains every two-dimensional normed space, Ann. Polon. Math. 49 (1988), 17-19. Zbl0679.46016

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