ON A CLASS OF KÖTHE SEQUENCE SPACES WITH NORMAL STRUCTURE

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (2): 576-590.

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ON A CLASS OF KÖTHE SEQUENCE SPACES WITH NORMAL STRUCTURE

B.Zlatanov

Department of Mathematics and Informatics, Plovdiv University, Bulgaria

Received:2009-03-26 Revised:2009-09-11 Online:2011-03-20 Published:2011-03-20
Supported by:
Research is partially supported by National Fund for Scientific Research of the Bulgarian Ministry of Education and Science, Contract MM-1401/04

Abstract

Abstract:

In this note, we investigate the generalized modulus of convexity δ^(λ) and the generalized modulus smoothness ρ^(λ). We obtain some estimates of these moduli for X=l_p. We obtain inequalities between WCS coefficient of a K\"othe sequence space X and δ_X^(λ). We show that, for a wide class of K\"othe sequence spaces X, if for some ε ∈(0, 9/10] holds δ_X(ε)>1/3(1-√3/2)ε, then X has normal structure.

Key words: Weakly convergent sequence coefficient, modulus of convexity, generalized modulus of convexity, normal structure

CLC Number:

46B20

B.Zlatanov . ON A CLASS OF KÖTHE SEQUENCE SPACES WITH NORMAL STRUCTURE[J].Acta mathematica scientia,Series B, 2011, 31(2): 576-590.

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ON A CLASS OF KÖTHE SEQUENCE SPACES WITH NORMAL STRUCTURE

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