# On the $H$-property of some Banach sequence spaces

Archivum Mathematicum (2003)

- Volume: 039, Issue: 4, page 309-316
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topSuantai, Suthep. "On the $H$-property of some Banach sequence spaces." Archivum Mathematicum 039.4 (2003): 309-316. <http://eudml.org/doc/249135>.

@article{Suantai2003,

abstract = {In this paper we define a generalized Cesàro sequence space $\operatorname\{ces\,\}(p)$ and consider it equipped with the Luxemburg norm under which it is a Banach space, and we show that the space $\operatorname\{ces\,\}(p)$ posses property (H) and property (G), and it is rotund, where $p = (p_k)$ is a bounded sequence of positive real numbers with $p_k > 1$ for all $k \in N$.},

author = {Suantai, Suthep},

journal = {Archivum Mathematicum},

keywords = {H-property; property (G); Cesàro sequence spaces; Luxemburg norm; property ; Cesàro sequence spaces; Luxemburg norm},

language = {eng},

number = {4},

pages = {309-316},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On the $H$-property of some Banach sequence spaces},

url = {http://eudml.org/doc/249135},

volume = {039},

year = {2003},

}

TY - JOUR

AU - Suantai, Suthep

TI - On the $H$-property of some Banach sequence spaces

JO - Archivum Mathematicum

PY - 2003

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 039

IS - 4

SP - 309

EP - 316

AB - In this paper we define a generalized Cesàro sequence space $\operatorname{ces\,}(p)$ and consider it equipped with the Luxemburg norm under which it is a Banach space, and we show that the space $\operatorname{ces\,}(p)$ posses property (H) and property (G), and it is rotund, where $p = (p_k)$ is a bounded sequence of positive real numbers with $p_k > 1$ for all $k \in N$.

LA - eng

KW - H-property; property (G); Cesàro sequence spaces; Luxemburg norm; property ; Cesàro sequence spaces; Luxemburg norm

UR - http://eudml.org/doc/249135

ER -

## References

top- Geometry of Orlicz spaces, Dissertationes Math., 1996, pp. 356. (1996) MR1410390
- On the Banach-Saks and weak Banach-Saks properties of some Banach sequence spaces, Acta Sci. Math. (Szeged ) 65 (1999), 179–187. (1999) MR1702144
- On some local geometry of Orlicz sequence spaces equipped the Luxemburg norms, Acta Math. Hungar. 80 (1-2) (1998), 143–154. (1998) MR1624558
- Banach-Saks property in some Banach sequence spaces, Annales Math. Polonici 65 (1997), 193–202. (1997) MR1432051
- Banach-Saks property and property ($\beta $) in Cesàro sequence spaces, SEA. Bull. Math. 24 (2000), 201–210. (2000) MR1810056
- Geometry of Banach Spaces - Selected Topics, Springer-Verlag, 1984. (1984) MR0461094
- Extreme and exposed points in Orlicz spaces, Canad. J. Math. 44 (1992), 505–515. (1992) MR1176367
- Orlicz spaces without strongly extreme points and without H-points, Canad. Math. Bull. 35 (1992), 1–5. (1992) MR1222531
- On some convexity properties of Orlicz sequence spaces, Math. Nachr. 186 (1997), 167–185. (1997) MR1461219
- Cesàro sequence spaces, Math. Chronicle, New Zealand 13 (1984), 29–45. (1984) Zbl0568.46006MR0769798
- Characterization of denting points, Proc. Amer. Math. Soc. 102 (1988), 526–528. (1988) MR0928972
- Method of sequence spaces, Guangdong of Science and Technology Press (1996 (in Chinese)). (1996 (in Chinese))
- Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, (1983). ((1983)) Zbl0557.46020MR0724434
- H-points and Denting Points in Orlicz Spaces, Comment. Math. Prace Mat. 33 (1993), 135–151. (1993) MR1269408
- On geometric properties of some Banach sequence spaces, Thesis for the degree of Master of Science in Mathematics, Chiang Mai University, 2000. (2000)
- Cesàro sequence spaces, Tamkang J. Math. 1 (1970), 143–150. (1970)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.