On the latticity of projection and antiprojection sets in Orlicz-Musielak spaces

被引：2

作者：

Micherda, B. ^{[1
]}

机构：

[1] Univ Bielsko Biala, Dept Math & Comp Sci, PL-43309 Bielsko Biala, Poland

来源：

ACTA MATHEMATICA HUNGARICA | 2008年 / 119卷 / 1-2期

关键词：

projection set; antiprojection set; latticially closed set; Orlicz-Musielak space;

D O I：

10.1007/s10474-007-7014-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the latticial structure of projection sets and antiprojection sets in Orlicz-Musielak spaces L-Phi, with the distance given by modular rho(Phi) and classical F-norms generated by rho(Phi). In particular, we show that the case of Amemiya F-norm is essentially different from others. This extends results given for sets of best approximants by Landers and Rogge, Kilmer and Kozlowski, and Mazzone.

引用

页码：165 / 180

页数：16

共 14 条

[1] On some proximinal subspaces of modular spaces [J].

Granero, AS ;

Hudzik, H .

ACTA MATHEMATICA HUNGARICA, 1999, 85 (1-2) :59-79

[2]

Isac G, 1998, MATH INEQUAL APPL, V1, P85

[3] On the property of four elements in modular spaces [J].

Isac, G ;

Lewicki, G .

ACTA MATHEMATICA HUNGARICA, 1999, 83 (04) :293-301

[4] BEST APPROXIMANTS IN MODULAR FUNCTION-SPACES [J].

KILMER, SJ ;

KOZLOWSKI, WM ;

LEWICKI, G .

JOURNAL OF APPROXIMATION THEORY, 1990, 63 (03) :338-367

[5]

KILMER SJ, 1991, COMMENT MATH U CAROL, V32, P241

[6]

KILMER SJ, 1991, COMMENT MATH HELV, V31, P59

[7]

Kuczma M, 1985, An introduction to the theory of functional equations and inequalities

[8] STRICTLY AND UNIFORMLY MONOTONE MUSIELAK-ORLICZ SPACES AND APPLICATIONS TO BEST APPROXIMATION [J].

KURC, W .

JOURNAL OF APPROXIMATION THEORY, 1992, 69 (02) :173-187

[9] A CHARACTERIZATION OF BEST PHI-APPROXIMANTS [J].

LANDERS, D ;

ROGGE, L .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 267 (01) :259-263

[10] BEST APPROXIMANTS IN LPHI-SPACES [J].

LANDERS, D ;

ROGGE, L .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1980, 51 (02) :215-237

← 1 2 →