Moduli of convexity and smoothness of reflexive subspaces of L期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Moduli of convexity and smoothness of reflexive subspaces of L

Authors:	S. Lajara

Affiliation:	^a Departamento de Matemáticas, Escuela de Ingenieros Industriales, Universidad de Castilla-La Mancha, Campus Universitario, 02071 Albacete, Spain ^b Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain

Abstract:	We show that for any probability measure μ there exists an equivalent norm on the space L¹(μ) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This renorming provides also an estimate for the corresponding modulus of smoothness of such subspaces.

Keywords:	Reflexive subspaces of mmlsi2" onclick=" submitCitation('/science?_ob=MathURL& _method=retrieve& _eid=1-s2.0-S0022123611002862& _mathId=si2.gif& _pii=S0022123611002862& _issn=00221236& _acct=C000051805& _version=1& _userid=1154080& md5=d0aa7c3e1da662a2719ed57bd10afa92')" style=" cursor:pointer " alt=" Click to view the MathML source" title=" Click to view the MathML source" > formulatext" title=" click to view the MathML source" >L¹ Uniformly convex Uniformly smooth Orlicz norm
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