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Structural Properties of Weak Cotype 2 Spaces

Published online by Cambridge University Press:  20 November 2018

Piotr Mankiewicz
Affiliation:
Institute of Mathematics Polish Academy of Sciences Śniadeckich8 00-950 Warsaw Poland e-mail: piotr@impan.impan.gov.pl
Nicole Tomczak-Jaegermann
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1 email: ntomczak@vega.math.ualberta.ca
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Abstract

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Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed proportional dimension are proved.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1996

References

[B] Bourgain, J., On finite-dimensional homogeneous Banach spaces, GAFA Israel Seminar 1986-87, Lecture Notes in Math. 1317, Springer, 232239.Google Scholar
[B-S] Bourgain, J. and Szarek, S.J., The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factorization, Israel J. Math. 62 (1988), 169180.Google Scholar
[Ma.1] Mankiewicz, P., Finite dimensional Banach spaces with symmetry constant of order y/n, Studia Math. 79 (1988), 193200.Google Scholar
[Ma.2. Mankiewicz, P., Subspace mixing properties of operators in ℝn with applications to Gluskin spaces, Studia Math. 88 (1988), 5167.Google Scholar
[Ma.3. Mankiewicz, P., Factoring the identity operator on a subspace of In , Studia Math. 95 (1989), 133139.Google Scholar
[M-T.1] Mankiewicz, P. and Tomczak, N.-Jaegermann, A solution of the finite-dimensional homogeneous Banach spaces problem, Israeli. Math. 75 (1991), 129159.Google Scholar
[M-T.2] Mankiewicz, P., Embedding subspaces of In , into spaces with Schauder basis, Proc. Amer. Math. Soc. 117 (1993), 459465.Google Scholar
[M-T.3] Mankiewicz, P., Schauder bases in subspaces of quotients ofli﹛X), Amer. J. Math., to appear.Google Scholar
[Mi] Milman, V.D., Inégalité de Brunn-Minkowski inverse et applications Íe théorie local des espaces normés, C. R. Acad. Sci. Paris Sér. 1 Math. 302 (1986), 2528.Google Scholar
[M-P] Milman, V.D. and Pisier, G., Banach spaces with weak cotype 2 property, Israel J. Math. 54 (1986), 139158.Google Scholar
[Pe.1] Pelczy, A.ński,Notes in Banach spaces, (ed. Lacey, H.E.), Univ. of Texas Press, Austin, 1980.Google Scholar
[P.1] Pisier, G., Holomorphic semi-groups and the geometry of Banach spaces, Ann. of Math. 115 (1982),375-392.Google Scholar
[P.2.] Pisier, G., On the duality between type and cotype, Martingale Theory in Harmonic Analysis and BanachGoogle Scholar
[P.3.] Pisier, G., spaces, Proceedings, Cleveland 1981, (eds. Chao, J.A. and Woyczynski, W.A.), Springer Lecture Notes 939, 131144. Volumes of Convex Bodies and Banach Spaces Geometry, Cambridge Univ. Press, 1989.Google Scholar
[Sz.1] Szarek, S.J., The finite dimensional basis problem with an appendix on nets of Grassmann manifolds, Acta Math. 151 (1983), 153179.Google Scholar
[Sz.2] Szarek, S.J., On the existence and uniqueness of complex structure and spaces with “few “ operators, Trans. Amer. Math. Soc. 293 (1986), 339353.Google Scholar
[T] Tomczak-Jaegermann, N., Banach-Mazur Distances and Finite Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Math., Longman Scientific & Technical, Harlow and John Wiley, New York, 1989.Google Scholar