zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Local rotundity structure of Cesàro--Orlicz sequence spaces. (English) Zbl 1155.46007
Summary: Some criteria for extreme points and strong U-points in Cesàro--Orlicz spaces are given. In consequence, we find a Cesàro--Orlicz sequence space different from $c_{0}$ which has no extreme points. Some examples show that in these spaces the notion of a strong U-point is essentially stronger than the notion of an extreme point. Various examples presented in this paper show that there are some differences between criteria for extreme points and strong U-points in Orlicz spaces and in Cesàro--Orlicz spaces. We also show that the uniqueness of the local best approximation needs the notion of an SU-point, that is, the notion of an extreme point is not strong enough here.

MSC:
46B20Geometry and structure of normed linear spaces
46B45Banach sequence spaces
WorldCat.org
Full Text: DOI
References:
[1] , Nieuw arch. Wiskd. 16, 47-51 (1968)
[2] Bandyopadhyay, P.; Huang, D.; Lin, B. L.: Rotund points, nested sequence of balls and smoothness in Banach spaces, Comment. math. 44, No. 2, 163-186 (2004) · Zbl 1097.46009
[3] Bennett, G.: Factorizing the classical inequalities, Mem. amer. Math. soc. 120, No. 576 (1996) · Zbl 0857.26009
[4] Chen, S. T.: Geometry of Orlicz spaces, Dissertationes math. (Rozprawy mat.) 356 (1996) · Zbl 1089.46500
[5] Chen, S. T.; Cui, Y. A.; Hudzik, H.; Sims, B.: Geometric properties related to fixed point theory in some Banach function lattices, , 339-389 (2001) · Zbl 1013.46015
[6] Cui, Y. A.; Hudzik, H.: Some geometric properties related to fixed point theory in Cesàro sequence spaces, Collect. math. 50, No. 3, 277-288 (1999) · Zbl 0955.46007
[7] Cui, Y. A.; Hudzik, H.: Packing constant for Cesàro sequence spaces, Nonlinear anal. 47, 2695-2702 (2001) · Zbl 1042.46505 · doi:10.1016/S0362-546X(01)00389-3
[8] Cui, Y. A.; Hudzik, H.; Meng, C.: On some local geometry of Orlicz sequence spaces equipped with the luxemburg norm, Acta math. Hungar. 80, No. 1 -- 2, 143-154 (1998) · Zbl 0914.46004 · doi:10.1023/A:1006533011548
[9] Cui, Y. A.; Hudzik, H.; Petrot, N.; Suantai, S.; Szymaszkiewicz, A.: Basic topological and geometric properties of Cesàro -- Orlicz spaces, Proc. indian acad. Sci. 115, No. 4, 461-476 (2005) · Zbl 1093.46013 · doi:10.1007/BF02829808
[10] Cui, Y. A.; Jie, L.; Płuciennik, R.: Local uniform nonsquareness in Cesàro sequence spaces, Comment. math. 37, 47-58 (1997) · Zbl 0898.46006
[11] Cui, Y. A.; Meng, C.; Płuciennik, R.: Banach -- Saks property and property $(\beta )$ in Cesàro sequence spaces, Southeast asian bull. Math. 24, 201-210 (2000) · Zbl 0956.46003
[12] Diestel, J.: Sequences and series in Banach spaces, Grad texts in math. 92 (1984) · Zbl 0542.46007
[13] P. Foralewski, H. Hudzik, R. Płuciennik, Orlicz spaces without extreme points, submitted for publication · Zbl 1194.46011
[14] P. Foralewski, H. Hudzik, A. Szymaszkiewicz, Some remarks on Cesàro -- Orlicz sequence spaces, submitted for publication · Zbl 1198.46017
[15] Grzaślewicz, R.; Hudzik, H.; Kurc, W.: Extreme and exposed points in Orlicz spaces, Canad. J. Math. 44, No. 3, 505-515 (1992) · Zbl 0766.46007 · doi:10.4153/CJM-1992-032-3
[16] Jagers, A. A.: A note on Cesàro sequence spaces, Nieuw arch. Wiskd. 22, 113-124 (1974) · Zbl 0286.46017
[17] Kantorovich, L. V.; Akilov, G. P.: Functional analysis, (1977) · Zbl 0127.06102
[18] Krasnoselskiı&caron, M. A.; ; Rutickiı&caron, Ya.B.; : Convex functions and Orlicz spaces, (1961)
[19] Lee, P. Y.: Cesàro sequence spaces, Math. chronicle New Zealand 13, 29-45 (1984) · Zbl 0568.46006
[20] Leibowitz, G. M.: A note on the Cesàro sequence spaces, Tamkang J. Math. 2, 151-157 (1971) · Zbl 0236.46012
[21] Lindenstrauss, J.; Tzafriri, L.: Classical Banach spaces I. Sequence spaces, (1977) · Zbl 0362.46013
[22] Lindenstrauss, J.; Tzafriri, L.: Classical Banach spaces II. Function spaces, (1979) · Zbl 0403.46022
[23] W.A.J. Luxemburg, Banach function spaces, thesis, Delft, 1955 · Zbl 0068.09204
[24] Maligranda, L.: Orlicz spaces and interpolation, Semin. math. 5 (1989) · Zbl 0874.46022
[25] Maligranda, L.; Petrot, N.; Suantai, S.: On the James constant and B-convexity of Cesàro and Cesàro -- Orlicz sequence spaces, J. math. Anal. appl. 326, 312-331 (2007) · Zbl 1109.46026 · doi:10.1016/j.jmaa.2006.02.085
[26] Musielak, J.: Orlicz spaces and modular spaces, Lecture notes in math. 1034 (1983) · Zbl 0557.46020
[27] Rao, M. M.; Ren, Z. D.: Theory of Orlicz spaces, (1991) · Zbl 0724.46032
[28] Shiue, J. S.: Cesàro sequence spaces, Tamkang J. Math. 1, 19-25 (1970) · Zbl 0215.19504