Support functionals and smooth points in abstract 𝑀 spaces

Baoxiang, Wang; Tingfu, Wang

doi:10.1090/S0002-9939-99-04771-1

Support functionals and smooth points in abstract $M$ spaces
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by Wang Baoxiang and Wang Tingfu PDF

Proc. Amer. Math. Soc. 127 (1999), 1761-1770 Request permission

Abstract:

By presenting some properties of support functionals in abstract $M$ spaces, we get some sufficient and necessary conditions for smooth points in abstract $M$ (function) spaces. Moreover, the notion of the smallest support semi-norm is introduced and an explicit form for this functional in abstract $M$ function spaces is also given.

References

Shu Tao Chen, Henryk Hudzik, and Anna Kamińska, Support functionals and smooth points in Orlicz function spaces equipped with the Orlicz norm, Math. Japon. 39 (1994), no. 2, 271–279. MR 1270637
Shu Tao Chen and Hui Ying Sun, Weak convergence and weak compactness in abstract $M$ spaces, Proc. Amer. Math. Soc. 123 (1995), no. 5, 1441–1447. MR 1273482, DOI 10.1090/S0002-9939-1995-1273482-1
Henryk Hudzik and Yi Ning Ye, Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm, Comment. Math. Univ. Carolin. 31 (1990), no. 4, 661–684. MR 1091364
Ep de Jonge, Representation of linear functionals on a class of normed Köthe spaces, J. Functional Analysis 23 (1976), no. 2, 119–134. MR 0423062, DOI 10.1016/0022-1236(76)90070-7
Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
L. V. Kantorovich and G. P. Akilov, Funktsional′nyĭ analiz, Izdat. “Nauka”, Moscow, 1977 (Russian). Second edition, revised. MR 0511615
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367, DOI 10.1007/978-3-662-35347-9
W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. Vol. I, North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1971. MR 0511676
Bao Xiang Wang, Support functional and its applications in Orlicz spaces, Comment. Math. (Prace Mat.) 33 (1993), 185–192. MR 1269413
Baoxiang Wang and Meilan Xu, On some applications of support functionals in Orlicz spaces, Comment. Math. (Prace Mat.) 35 (1995), 235–244. MR 1384870
B. X. Wang and T. F. Wang, The characteristic of weak convergence in a class of Banach sequence lattices, Collect. Math. 48 (1997), 799–807.
Xintai Yu, Geometry of Banach Spaces, Shanghai, 1986.
A. C. Zaanen, Riesz spaces. II, North-Holland Mathematical Library, vol. 30, North-Holland Publishing Co., Amsterdam, 1983. MR 704021, DOI 10.1016/S0924-6509(08)70234-4