# 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

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topChalmers, 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

top- [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
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- [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] 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] H. Koenig, Projections onto symmetric spaces, Quaestiones Math. 18 (1995), 199-220. Zbl0827.46005
- [6] J. Lindenstrauss, On the extension of operators with a finite-dimensional range, Illinois J. Math. 8 (1964), 488-499. Zbl0132.09803
- [7] N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Wiley, New York, 1989.
- [8] D. Yost, L₁ contains every two-dimensional normed space, Ann. Polon. Math. 49 (1988), 17-19. Zbl0679.46016

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