Multiplication Operators On Grand Lorentz Spaces

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Let (X,∑,µ ) be a δ -finite measure space, f be a complex-valuedmeasurable function defined on X and u : X → be a measurable function suchthat u. f ∈ M (X,∑) whenever f ∈ M (X,∑) where M (X,∑) is the set of allmeasurable functions defined on X . This gives rise to a linear transformationMu: M (X,∑) → M (X,∑) defined by Mu (f) = u.f , where the product offunctions is pointwise. In case if M (X,∑) is a topological vector space and Mu isa continuous (bounded) operator, then it is called a multiplication operator inducedby u . In this paper, multiplication operators on grand Lorentz spaces are definedand the fundamental properties such as boundedness, closed range, invertibility,compactness and closedness of these are characterized.

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Grand Lorentz space , Multiplication operator , Compact operator

Erciyes University Journal Of The Institute Of Science an‎d Technology

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Erciyes University Journal Of The Institute Of Science an‎d Technology