Symmetric subspaces of $l_1$ with large projection constants

ArticleOriginal scientific text

Title

Authors ¹, ²

Department of Mathematics, University of California Riverside, California 92521, U.S.A.
Department of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

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}) \geq λ (V^{k}, l_{1}) > λ (l_{2}^{(k)})

.

[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.
[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.
[CHM2] B. L. Chalmers and F. T. Metcalf, A characterization and equations for minimal projections and extensions, J. Operator Theory 32 (1994), 31-46.
[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.
[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.
[HK] H. Koenig, Projections onto symmetric spaces, Quaestiones Math. 18 (1995), 199-220.
[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.
[RU] D. Rutovitz, Some parameters associated with finite-dimensional Banach spaces, J. London Math. Soc. 40 (1965), 241-255.
[NT] N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Wiley, New York, 1989.
[WO] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, 1991.