Orlicz空间上的完全连续复合算子（英文）
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摘要
设φ:X→X是非奇异变换,Ψ是Orlicz函数,(X,∑,μ)是完备的σ-有限测度空间.本文利用Radon-Nikodym导数(dμoφ~(-1))/dμ刻画了Orlicz空间上紧的复合算子C_φ,同时给出了该空间上有界复合算子完全连续的充要条件.
Let φ:X→X be a non-singular transformation,Ψ be an Orlicz function and(X,∑,μ) a complete σ-finite measure space.In this paper,by using Radon-Nikodym derivative(dμoφ~(-1))/dμ,the compact composition operator C_φf =foφ on Orlicz space L~Ψ(μ) is characterized.The sufficient and necessary condition for the bounded composition operator to be completely continuous is obtained.
Let φ:X→X be a non-singular transformation,Ψ be an Orlicz function and(X,∑,μ) a complete σ-finite measure space.In this paper,by using Radon-Nikodym derivative(dμoφ~(-1))/dμ,the compact composition operator C_φf =foφ on Orlicz space L~Ψ(μ) is characterized.The sufficient and necessary condition for the bounded composition operator to be completely continuous is obtained.
引文
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[2]Cowen,C.C.and MacCluer,B.D.,Composition operators on spaces of analytic functions,New York:CRC Press,1995.
[3]Cui,Y.A.,Hudzik,H.,Kumar,R.and Maligranda,L.,Composition operators in Orlicz spaces,J.Aust.Math.Soc.,2004,76(2):189-206.
[4]Jabbarzadeh,M.R.,A note on weighted composition operators on measurable function spaces,J.Korean Math.Soc,2004,41(1):95-105.
[5]Jabbarzadeh,M.R.,The essential norm of a composition operator on Orlicz spaces,Turk.J.Math.,2010,34(4):537-542.
[6]Komal,B.S.and Gupta,S.,Composition operators on Orlicz spaces,Indian J.Pure Appl.Math.,2001,32(7):1117-1122.
[7]Kumar,R.,Composition operators on Orlicz spaces,Integral Equations Operator Theory,1997,29(1):17-22.
[8]Rao,M.M.and Ren,Z.D.,Theory of Orlicz Spaces,New York:Marcel Dekker,1991.
[9]Shapiro,J.H.,Composition Operators and Classical Function Theory,New York:Springer-Verlag,1993.
[2]Cowen,C.C.and MacCluer,B.D.,Composition operators on spaces of analytic functions,New York:CRC Press,1995.
[3]Cui,Y.A.,Hudzik,H.,Kumar,R.and Maligranda,L.,Composition operators in Orlicz spaces,J.Aust.Math.Soc.,2004,76(2):189-206.
[4]Jabbarzadeh,M.R.,A note on weighted composition operators on measurable function spaces,J.Korean Math.Soc,2004,41(1):95-105.
[5]Jabbarzadeh,M.R.,The essential norm of a composition operator on Orlicz spaces,Turk.J.Math.,2010,34(4):537-542.
[6]Komal,B.S.and Gupta,S.,Composition operators on Orlicz spaces,Indian J.Pure Appl.Math.,2001,32(7):1117-1122.
[7]Kumar,R.,Composition operators on Orlicz spaces,Integral Equations Operator Theory,1997,29(1):17-22.
[8]Rao,M.M.and Ren,Z.D.,Theory of Orlicz Spaces,New York:Marcel Dekker,1991.
[9]Shapiro,J.H.,Composition Operators and Classical Function Theory,New York:Springer-Verlag,1993.