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A WEAK HILBERT SPACE THAT IS A TWISTED HILBERT SPACE

Part of: Normed linear spaces and Banach spaces; Banach lattices Methods of category theory in functional analysis

Published online by Cambridge University Press:  15 May 2018

Jesús Suárez de la Fuente
Jesús Suárez de la Fuente*
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06011 Badajoz, Spain (jesus@unex.es)
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Abstract

We construct a weak Hilbert space that is a twisted Hilbert space.

Keywords

weak Hilbertinterpolationtwisted sumcentralizer

MSC classification

Primary: 46B20: Geometry and structure of normed linear spaces 46B06: Asymptotic theory of Banach spaces
Secondary: 46B70: Interpolation between normed linear spaces 46M18: Homological methods (exact sequences, right inverses, lifting, etc.) 46B45: Banach sequence spaces
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 3 , May 2020 , pp. 855 - 867
Copyright
© Cambridge University Press 2018

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Footnotes

The author was supported in part by project MTM2016-76958-C2-1-P and project IB16056 of La Junta de Extremadura.

References

Albiac, F. and Kalton, N. J., Topics in Banach Space Theory, Graduate Texts in Mathematics, Volume 233 (Springer, New York, 2006).Google Scholar
Androulakis, G., Casazza, P. G. and Kutzarova, D. N., Some more weak Hilbert spaces, Canad. Math. Bull. 43(3) (2000), 257–267.Google Scholar
Anisca, R., The ergodicity of weak Hilbert spaces, Proc. Amer. Math. Soc. 138(4) (2010), 1405–1413.Google Scholar
Bergh, J. and Löfström, J., Interpolation Spaces. An Introduction, Grundlehren der Mathematischen Wissenschaften, No 223 (Springer-Verlag, Berlin–New York, 1976).Google Scholar
Cabello Sánchez, F., Nonlinear centralizers in homology, Math. Ann. 358(3–4) (2014), 779–798.Google Scholar
Calderón, A. P., Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190.Google Scholar
Carro, M. J., Cerdà, J. and Soria, J., Commutators and interpolation methods, Ark. Mat. 33(2) (1995), 199–216.Google Scholar
Casazza, P. G. and Nielsen, N. J., The Maurey extension property for Banach spaces with the Gordon–Lewis property and related structures, Studia Math. 155(1) (2003), 1–21.Google Scholar
Casazza, P. and Shura, T. J., Tsirelson’s Space. With an Appendix by J. Baker, O. Slotterbeck and R. Aron, Lecture Notes in Mathematics, Volume 1363 (Springer-Verlag, Berlin, 1989).Google Scholar
Castillo, J. M. F., Ferenczi, V. and González, M., Singular twisted sums generated by complex interpolation, Trans. Amer. Math. Soc. 369 (2017), 4671–4708.Google Scholar
Castillo, J. M. F. and González, M., Three-Space Problems in Banach Space Theory, Lecture Notes in Mathematics, Volume 1667 (Springer-Verlag, 1997).Google Scholar
Castillo, J. M. F. and Plichko, A., Banach spaces in various positions, J. Funct. Anal. 259(8) (2010), 2098–2138.Google Scholar
Cobos, F. and Schonbek, T., On a theorem by Lions and Peetre about interpolation between a Banach space and its dual, Houston J. Math. 24(2) (1998), 325–344.Google Scholar
Corrêa, W., Type, cotype and twisted sums induced by complex interpolation, J. Funct. Anal. 274(3) (2018), 797–825.Google Scholar
Cuellar-Carrera, W., Non-ergodic Banach spaces are near Hilbert, Trans. Amer. Math. Soc. (to appear). doi:10.1090/tran/7319.Google Scholar
Edgington, A., Some more weak Hilbert spaces, Studia Math. 100(1) (1991), 1–11.Google Scholar
Enflo, P., Lindenstrauss, J. and Pisier, G., On the ‘three space problem’, Math. Scand. 36(2) (1975), 199–210.Google Scholar
Johnson, W. B., Banach spaces all of whose subspaces have the approximation property. Seminar on Functional Analysis, 1979–1980 (French), Exp. No. 16, 11 pp., École Polytech., Palaiseau, 1980.Google Scholar
Kalton, N. J., Differentials of complex interpolation processes for Köthe function spaces, Trans. Amer. Math. Soc. 333(2) (1992), 479–529.Google Scholar
Kalton, N. J., Twisted Hilbert spaces and unconditional structure, J. Inst. Math. Jussieu 2(3) (2003), 401–408.Google Scholar
Kalton, N. J. and Peck, N. T., Twisted sums of sequence spaces and the three space problem, Trans. Amer. Math. Soc. 255 (1979), 1–30.Google Scholar
Komorowski, R., On constructing Banach spaces with no unconditional basis, Proc. Amer. Math. Soc. 120(1) (1994), 101–107.Google Scholar
Komorowski, R. A. and Tomczak-Jaegermann, N., Banach spaces without local unconditional structure, Israel J. Math. 89(1–3) (1995), 205–226.Google Scholar
Kwapień, S., Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math. 44 (1972), 583–595.Google Scholar
Mascioni, V., On weak cotype and weak type in Banach spaces, Note Mat. 8(1) (1988), 67–110.Google Scholar
Mascioni, V., On Banach spaces isomorphic to their duals, Houston J. Math. 19(1) (1993), 27–38.Google Scholar
Milman, V. D. and Pisier, G., Banach spaces with a weak cotype 2 property, Israel J. Math. 54 (1986), 139–158.Google Scholar
Odell, E. and Schlumprecht, Th., Trees and branches in Banach spaces, Trans. Amer. Math. Soc. 354(10) (2002), 4085–4108.Google Scholar
Pisier, G., Weak Hilbert spaces, Proc. Lond. Math. Soc. (3) 56 (1988), 547–579.Google Scholar
Pisier, G., Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracts in Mathematics, Volume 94 (Cambridge University Press, Cambridge, 1989).Google Scholar
Pisier, G., Factorization of Linear Operators and Geometry of Banach Spaces, CBSM Regional Conference Series in Mathematics, Volume 60 (American Mathematical Society, Providence, RI, 1986).Google Scholar
Tomczak-Jaegermann, N., Computing 2-summing norm with few vectors, Ark. Mat. 17(2) (1979), 273–277.Google Scholar