Relations between some constants associated with finite dimensional Banach spaces. (English) Zbl 0212.14203


46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B03 Isomorphic theory (including renorming) of Banach spaces
Full Text: DOI


[1] A. Dvoretzky and C. A. Rogers,Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A.36, (1950), 192–197. · Zbl 0036.36303
[2] D. J. H. Garling,Symmetric bases of locally convex spaces, Studia Math.30 (1968), 163–181. · Zbl 0159.17703
[3] D. J. H. Garling,Absolutely p-summing operators in Hilbert space, to appear in Studia Math. · Zbl 0203.45502
[4] Y. Gordon,On the projection and Macphail constants of l n p spaces, Israel J. Math.6 (1968), 295–302. · Zbl 0182.45202
[5] Y. Gordon,On p-absolutely summing constants of Banach spaces, Israel J. Math.7 (1969), 151–163. · Zbl 0179.17502
[6] A. Grothendieck,Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. Sāo Paulo8 (1956), 1–79.
[7] B. Grünbaum,Projection constants, Trans. Amer. Math. Soc.95 (1960), 451–465. · Zbl 0095.09002
[8] V. I. Gurarii, M. I. Kadec, and V.I. Macaev,On Banach-Mazur distance between certain Minkowsky spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.13 (1965), 719–722.
[9] V. I. Gurarii, M. I. Kadec, and V. I. Maeaev,Distances between finite-dimensional analogs of the L p -spaces, Mat. Sb.70 (112) (1966), 481–489 (Russian).
[10] V. I. Gurarii, M. I. Kadec, and V. I. Macaev,Dependence of certain properties of Minkowski spaces on asymmetry. Mat. Sb.71 (113) (1966), 24–29 (Russian).
[11] F. John,Extremum problems with inequalities as subsidiary conditions, Courant Anniversary Volume, 187–204, Interscience, New York, 1948.
[12] J. L. Kelley,Banach spaces with the extension property, Trans. Amer. Math. Soc.72 (1952), 323–326. · Zbl 0046.12002
[13] J. Lindenstrauss and A. Pełczyński,Absolutely summing operators in p spaces and their applications, Studia Math.29 (1968), 275–326. · Zbl 0183.40501
[14] A. Persson and A. Pietsch,p-nukleare und p-integrale Abbildungen in Banachraumen, Studia Math.33 (1969), 19–62.
[15] A. Pietsch,Absolute p-summierende Abbildungen in normierten Raumen, Studia Math.28 (1967), 333–353. · Zbl 0156.37903
[16] D. Rutovitz,Some parameters associated with finite-dimensional Banach spaces, J. London Math. Soc.40 (1965), 241–255. · Zbl 0125.06402
[17] I. Singer,Some characterizations of symmetric bases in Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.10 (1962), 185–192. · Zbl 0119.10005
[18] A. Zygmund,Trigonometric Series, Vol.1, 2nd Ed., Cambridge, 1959. · Zbl 0085.05601
[19] E.W. Cheney and K.H. Price,Minimal projections, Approximation theory conference, Lancaster, England, 1968.
[20] M. I. Kadec, to appear inFunktional Analiz. i Prilož.
[21] W. J. Davies,Remarks on finite rank projections (to appear).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.