The Journal of the Indian Mathematical Society

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Vector Valued Multipliers of McShane Integrable Functions


Affiliations
1 Department of Mathematics, Panjab University, Chandigarh, India, India
     

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We study the algebra of vector valued multipliers of Banach algebra valued McShane integrable functions. We prove that if X is a commutative Banach algebra, with identity e of norm one, then functions associated with measures of strong bounded variation and the set {L?([a, b],?) e} are vector valued multipliers of McShane integrable functions. We find some necessary and another set of sufficient conditions for a functiong to define a multiplier. In case X satisfies Radon Nikodym property (weak Radon Nikodym property), we study multiplier operators.


Keywords

McShane Integrable, Banach Algebra, Multiplier, Radon Nikodym Property.
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  • Vector Valued Multipliers of McShane Integrable Functions

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Authors

Savita Bhatnagar
Department of Mathematics, Panjab University, Chandigarh, India, India

Abstract


We study the algebra of vector valued multipliers of Banach algebra valued McShane integrable functions. We prove that if X is a commutative Banach algebra, with identity e of norm one, then functions associated with measures of strong bounded variation and the set {L?([a, b],?) e} are vector valued multipliers of McShane integrable functions. We find some necessary and another set of sufficient conditions for a functiong to define a multiplier. In case X satisfies Radon Nikodym property (weak Radon Nikodym property), we study multiplier operators.


Keywords


McShane Integrable, Banach Algebra, Multiplier, Radon Nikodym Property.

References





DOI: https://doi.org/10.18311/jims%2F2022%2F29294