Two-dimensional real symmetric spaces with maximal projection constant

• Autorzy: Bruce L. Chalmers , Grzegorz Lewicki
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

absolute projection constant; minimal projection; symmetric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 73
• Numer: 2
• Strony: 119-134

Daty

wydano

2000

otrzymano

1998-12-02

poprawiono

1999-10-27

Twórcy

autor

Bruce L. Chalmers

• Department of Mathematics, University of California, Riverside, CA, 92521, U.S.A.

autor

Grzegorz Lewicki

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [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.
• [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.
• [3] B. L. Chalmers and F. T. Metcalf, A characterization and equations for minimal projections and extensions, J. Operator Theory 32 (1994), 31-46.
• [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.
• [5] H. Koenig, Projections onto symmetric spaces, Quaestiones Math. 18 (1995), 199-220.
• [6] J. Lindenstrauss, On the extension of operators with a finite-dimensional range, Illinois J. Math. 8 (1964), 488-499.
• [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.