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The notions of metrical and topological vector boundedness of sets are considered in Musielak-Orlicz spaces. The space is called right if both these notions are equivalent. Necessary conditions of the rightness are established, and certain sufficient conditions are found.
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Czasopismo
Rocznik
Tom
Strony
305--312
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
Bibliografia
- [1] N. Dunford and J.T. Schwartz, Linear operators, p.1: General theory, Intersc. Publ., 1958.
- [2] A. Kolmogoroff, Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes, Stud. Math. 5 (1934), 29–33.
- [3] V.L. Levin, Measurable cross-sections of multivalued mappings and projections of measurable sets, Funct. Anal.i Prilozh. 12:2 (1978) 40–45 (in Russian) [English translation: Funct. Anal. Appl. 12:2 (1978) 108-112].
- [4] S. Mazur and W. Orlicz, Über Folgen linearen Operatoren, Studia Math. 3 (1933), 152–157.
- [5] J. Musielak, Orlicz spaces and modular spaces, Springer-Verlag, 1983.
- [6] J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18:1 (1959), 49-65.
- [7] J. von Neumann, On complete topological spaces, Trans. Amer. Math. Soc. 37 (1935), 1–20.
- [8] D. Przeworska-Rolewicz and S. Rolewicz, Historical remarks on bounded sets, European mathematics in the last centuries, Univ. Wroclaw, 2005, 87–97.
- [9] S. Rolewicz, Metric linear spaces, Polish Sci. Publ. and D. Reidel, 1985.
- [10] W. Rudin Functional analysis, McGraw-Hill book comp., 1973.
- [11] I.V. Shragin, On some theorem on measurable selection, Comment. Math. 47:2 (2007), 221–225.
- [12] K. Yosida, Functional analysis, Springer-Verlag, 1965.
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Bibliografia
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