Affiliation:
1. Department of Mathematics Anhui Normal University Wuhu Anhui China
2. Smeal College Pennsylvania State Universi University Park Pennsylvania USA
3. Department of Mathematics Shanghai University Shanghai China
Abstract
AbstractIn this work, we give three kinds of criteria for weak sets in Orlicz–Bochner sequence spaces without constraints, conditions posited in each criterion are necessary and sufficient. As an application, we give criteria for weak sets in Orlicz sequence spaces. Well‐known conclusions are exhibited once more, such as Schur's theorem, Banach–Alaoglu's theorem, and the boundedly compact principle of finite dimension space. The results obtained show that the weak compactness may not be extrapolated straightforwardly from to , for example, .
Funder
National Natural Science Foundation of China
Reference30 articles.
1. P. S.AleksandrovandA. N.Kolmogorov Vvedenie v teoriyu mnoz̆estv i teoriyu funkciĭ. C̆ast́ pervaya. = Vvedenie v obs̆c̆uyu teoriyu mnoz̆estv i funkciĭ. [Introduction to the Theory of Sets and the Theory of Functions. Part One. = Introduction to the General Theory of Sets and Functions] Gosudarstv. Izdat. Tehn.‐Teor. Lit. Moscow‐Leningrad 1948.
2. Weakly Compact Sets in Orlicz Spaces
3. Note on Series of Analytic Functions
4. Le curve limiti di una varieta' data di curve[in italian];Ascoli G.;Rend. Accad. Lincei,1884
5. Invarianz des n‐dimensionalen cabiets;Brouwer L.;Math. Ann.,1912