Abstract
We calculate the measure of non-compactness or the essential norm of the multiplication operator Mu acting on Orlicz sequence spaces lφ. As a consequence of our result, we obtain a known criteria for the compactness of multiplication operator acting on lφ.
Highlights
Let (Ω, Σ) = (Ω, Σ, μ) be a complete σ-finite measure space and let L0(μ) denote the space of all μ-equivalence classes of Σ-measurable functions on Ω with the topology of convergence in measure on μ-finite sets
A Kothe space defined on N, 2N, μ with the counting measure μ is called a Kothe sequence space
We must mention here the pioneering work Singh/Kumar in [12] and [13] on properties of multiplication operators acting on spaces of measurable functions
Summary
We must mention here the pioneering work Singh/Kumar in [12] and [13] on properties of multiplication operators acting on spaces of measurable functions. These authors studied the compactness and closedness of the range of multiplication operators on L2(μ). Related to the problem of the characterization of the compactness of multiplication operators we have the problem of to estimate its essential norm or the non-compactness measure of multiplication operators This subject has been widely studied in the context of analytic functions. The essential norm of multiplication operators acting on Lorentz sequence spaces (which is a Kothe sequence space) was calculate by Castillo et al [4].
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