Fenchel-Orlicz spaces

Turett, Barry

Książka - szczegóły

Tytuł książki

Fenchel-Orlicz spaces

Autorzy

Barry Turett

Seria

Rozprawy Matematyczne tom/nr w serii: 181 wydano: 1980

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Warianty tytułu

Abstrakty

CONTENTS

Introduction............................................................................... 5
1. Definitions and preliminary results......................................... 7
2. Completeness of $L^Φ(μ, \mathfrak{R})$.............................. 9
3. Linear functionals on $L^Φ(μ, \mathfrak{R})$....................... 26
4. Geometry of Fenchel-Orlicz spaces........................................ 41
References....................................................................................... 54

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 181

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CLXXXI

Daty

wydano

1980

Twórcy

autor

Barry Turett

Bibliografia

[1] E. Asplund, Fréchet differentiability of convex functions, Acta Math. 121 (1968), pp. 31-47.
[2] E. Asplund, and R. T. Rockafellar, Gradients of convex functions, Trans. Amer. Math. Soc. 139 (1969), pp. 443-467.
[3] R. G. Bartle, A general bilinear vector integral, Studia Math. 15 (1955), pp. 337-352.
[4] Z. Birnbaum, and W. Orlicz, Über die Verallgemeinerung des Begriffes der zueinander konjugatierten Potenzen, Studia Math. 3 (1931), pp. 1-67.
[5] S. Bochner, Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind, Fund. Math. 20 (1933), pp. 262-276.
[6] A. Brøndsted, Conjugate convex functions in topological vector spaces, Mat.-Fys. Medd. Dansk. Vid. Selsk. 34 (2) (1964), pp. 1-26.
[7] A. Brøndsted, and R. T. Rockafellar, On the subdifferentiability of convex functions, Proc. Amer. Math. Soc. 16 (1965), pp. 605-611.
[8] W. J. Davis, T. Fiegiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), pp. 311-327.
[9] M. M. Day, Normed Linear Spaces, Third Edition, Springer-Verlag, Berlin-Heidelberg-New York 1973.
[10] J. Diestel, J. and J.J. Uhl, Jr., Vector Measures, AMS Math. Surveys, No. 15, 1977.
[11] N. Dunford, and J. T. Schwartz, Linear Operators, Part I, Interscience, New York 1958.
[12] W. Fenchel, On conjugate convex functions, Canad. J. Math. 1 (1949), pp. 73-77.
[13] A. D. Ioffe, B-spaces generated by convex integrands, and multidimensional variation problems, Soviet Math. Dokl. 11 (1970), pp. 1600-1604.
[14] A. D. Ioffe, Banach spaces generated by convex integrals, Optimization 3 (1971), pp. 47-86 (Russian).
[15] P. Kosmol, Flache Konvexität von Orliczräumen, Colloquium Math. 31 (1974), pp. 249-252.
[16] G. Köthe, Topological Vector Spaces I, Springer-Verlag, Berlin 1969.
[17] A. Kozek, Orlicz spaces of functions with values in Banach spaces, Commentationes Math. 19 (1977), pp. 259-288.
[18] M. A. Krasnosel'skii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces (translation), P. Noordhoof, Ltd., Groningen 1961.
[19] I. E. Leonard and K. Sundaresan, Geometry of Lebesgue-Bochner function spaces-smoothness, Bull. Acad. Math. Soc. 79 (1973), pp. 546-549.
[20] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Springer-Verlag, Berlin-Heidelberg-New York 1973.
[21] W. A. J. Luxemburg, Banach Function Spaces, Delft 1955.
[22] J. J. Moreau, Fonctions convex en dualité, Séminaires de Mathématiques, Faculté des Sciences, Université de Montpellier (1962).
[23] J. J. Moreau, Fonctionnelles Convexes, Séminaire équations aux dérivées partielles, Collège de France (1966).
[24] J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18 (1959), pp. 49-65.
[25] J. Musielak and W. Orlicz, Some remarks on modular spaces, Bull. Acad. Polon. Sei. Sér. Sci. Math. Astronom. Phys. 7 (1959), pp. 661-668.
[26] H. Nakano, Modulared semi-ordered linear spaces, Tokyo Math. Book Series, Vol. 1, 1950.
[27] H. Nakano, Generalized modular spaces, Studia Math. 31 (1968), pp. 439-449.
[28] W. Orlicz, Über eine gewisse Klasse von Rallmen vom Typus B, Bull. Int. Acad. Polon. Sci., Ser. A. (1932), pp. 207-220.
[29] G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), pp. 326-350.
[30] V. R. Portnov, Some properties of Orlicz spaces generated by M(x, w) functions, Soviet Math. Dokl, 7 (1966), pp. 1377-1380.
[31] M. M. Rao, Smoothness of Orlicz spaces, Proc. Acad. Amsterdam, A68 (1965), pp. 671-690.
[32] R. T. Rockafellar, Convex Analysis, Princeton 1970.
[33] M. S. Skaff, Vector valued Orlicz spaces. Generalized N-functions, I, Pacific J. Math. 28 (1969), pp. 193-206.
[34] M. S. Skaff, Vector valued Orlicz spaces II, Pacific J. Math. 28 (1969), pp. 413-430.
[35] K. Sundaresan, On the strict and uniform convexity of certain Banach spaces, Pacific J. Math. 15 (1965), pp. 1083-1086.
[36] B. Turett, Rotundity of Orlicz spaces, Proc. Acad. Amsterdam, A 79 (1976), pp. 462-469.
[37] B. Turett and J. J. Uhl, Jr., $L_p(μ, X)$ (1 < p < ∞) has the Radon-Nikodym property, if X does by martingales, Proc. Amer. Math. Soc. 61 (1976), pp. 347-350.
[38] J. J. Uhl, Jr., Orlicz spaces of finitely additive set functions, Studia Math. 29 (1967), pp. 19-58.
[39] G. Weiss, A note on Orlicz spaces, Portugaliae Math. 15 (1956), pp. 35-47.
[40] A. C. Zaanen, Linear Analysis, North Holland, Amsterdam 1953.

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bwmeta1.element.zamlynska-d9dff287-0135-4ff6-91df-a39a66041945

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83-01-01117-3

ISSN

0012-3862

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