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Definition of Symmetric Spaces Read chapter Read first chapter

2016 | OriginalPaper | Chapter

8. Maximality. Properties (B) and (C)

Authors : Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova

Published in: Foundations of Symmetric Spaces of Measurable Functions

Publisher: Springer International Publishing

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Abstract

In this chapter, we study the second associate space X 11 of a symmetric space X. To describe properties of the natural embedding X ⊆ X 11, we two consider important properties (B) and (C) of the space X. We show that X has property (C) if and only if the natural embedding X → X 11 is isometric. If in addition to (C), X has property (B), then X = X 11, i.e., the symmetric space X is maximal, and the natural embedding X → X 11 is an isometric isomorphism between X and X 11.

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previous chapter Associate Spaces
next chapter Lorentz Spaces
Literature
2.
3.
Bennett, C., Sharpley, R.: Interpolation of Operators. Pure and Applied Mathematics, vol. 129. Academic Press Professional, Boston (1988)
4.
Bergh, J., Löfström, J.: Interpolation spaces: an introduction, Grundlehren der mathematischen Wissenschaften, vol. 223. Springer, Berlin (1976)MATH
7.
8.
Bukhvalov, A., Veksler, A., Geiler, V.: Normed lattices. J. Sov. Math. 18 (4), 516–551 (1982)CrossRefMATH
9.
Bukhvalov, A., Veksler, A., Lozanovskii, G.: Banach lattices: some aspects of their theory. Russ. Math. Surv. 34 (2), 159–212 (1979). [In Russian: Uspehi Mat. Nauk 34 2(206), (1979), 137–183]
10.
Burenkov, V.: Function spaces: main integral inequalities connected with the spaces lp. Moscow Publishing House of the University of Friendship of Nations (1989)
11.
Calderón, A.: Spaces between l 1 and l ∞ and the theorem of marcinkiewicz. Stud. Math. 26 (3), 273–299 (1966)MathSciNetMATH
14.
Chong, K., Rice, N.: Equimeasurable Rearrangements of Functions. Queen’s Papers in Pure and Applied Mathematics, vol. 28. National Library of Canada (1971)
16.
Day, P.: Rearrangements of measurable functions. Ph.D. Thesis, California Institute of Technology (1970)
27.
Hardy, G., Littlewood, J., Pólya, G.: Inequalities. Cambridge university press, Cambridge (1952)MATH
29.
Johnson, W., Maurey, B., Schechtman, G., Tzafriri, L.: Symmetric Structures in Banach Spaces. American Mathematical Society: Memoirs of the American Mathematical Society, vol. 217 American Mathematical Society (1979)
31.
Kantorovich, L., Akilov, G.: Functional Analysis in Normed Spaces. International Series of Monographs in Pure and Applied Mathematics, vol. 46, xiii, 773 p. Pergamon Press, Oxford/London/New York/Paris/Frankfurt (1964); Translated from the Russian by D. E. Brown. Edited by A. P. Robertson (English). Zbl 0127.06104
32.
Kantorovich, L., Vulikh, B., Pinsker, A.: Functional analysis in semi-ordered spaces, 548 pp. Gosudarstv. Izdat. Tekhn.-Teor. Lit., Moskva-Leningrad (1950); In Russian: Functional Analisys. Nauka, Moscow (1977)
34.
Krein, S.G., Petunin, Y.I., Semenov, E.M.: Interpolation of Linear Operators. Translations of Mathematical Monographs, vol. 54. American Mathematical Society, Providence (1982). In Russian: Nauka, Moscow (1978)
35.
Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces: sequence spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 92. Springer, New York (1977)
36.
Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces: function spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 97. Springer, New York (1979)
42.
Luxemburg, W.A.J.: Banach function spaces. Getal en Figuur. 6, 70 p. Van Gorcum & Comp, Assen/Delft (1955). Zbl 0068.09204 (English)
46.
Meyer-Nieberg, P.: Banach Lattices. Universitext. Springer, Berlin/Heidelberg (2012)MATH
47.
Mityagin, B.: An interpolation theorem for modular spaces. Mat. Sb. 108 (4), 473–482 (1965)MathSciNet
51.
Nakano, H.: Modulared Semi-Ordered Linear Spaces. Maruzen Co. Ltd., Tokyo (1950)MATH
56.
Pick, L., Kufner, A., John, O., Fucík, S.: Function Spaces, vol. 1. Walter de Gruyter (2012)
65.
Schaefer, H.: Banach Lattices and Positive Operators. Springer, New York/Heidelberg (1974); Die Grundlehren der mathematischen Wissenschaften, Band 215
66.
Schwarz, H.: Banach Lattices and Operators, Teubner-Texte zur Mathematik, Band 71. B.G. Teubner, Leibzig (1984)
75.
Vulikh, B.Z.: Introduction to the Theory of Partially Ordered Spaces, xv, 387 p. Wolters-Noordhoff Scientific Publications Ltd., Groningen (1967). In Russian: Gosizdat phis-math lit., Moscow, (1961); Translated from the Russian by Leo F. Boron, with the editorial collaboration of Adrian C. Zaanen and Kiyoshi Iséki. Zbl 0186.44601 (English)
78.
Zaanen, A.: Integration. North Holland Publishing Company, Amsterdam (1967)MATH
79.
Zaanen, A.: Riesz Spaces II. North-Holland Mathematical Library. Elsevier Science, Amsterdam (1983)MATH
Metadata
Title
Maximality. Properties (B) and (C)
Authors
Ben-Zion A. Rubshtein
Genady Ya. Grabarnik
Mustafa A. Muratov
Yulia S. Pashkova
Copyright Year
2016
Book
Foundations of Symmetric Spaces of Measurable Functions

Print ISBN: 978-3-319-42756-0

Electronic ISBN: 978-3-319-42758-4

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-42758-4_8

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