The Journal of the Indian Mathematical Society

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Local Spectral Properties of a Composition Operator on LP Spaces


Affiliations
1 Department of Mathematics, Banaras Hindu University Varanasi, 221005, India
2 Department of Mathematics and DST-CIMS, Banaras Hindu University, Varanasi, 221005, India
     

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In this paper, we discuss the decomposability and single valued extension property of composition operators Cφ on Lp(X)(1 ≤ p < ∞) spaces. We give a sufficient condition for non-decomposability of Cφ in terms of Radon-Nikodym derivative. Further, we prove that if φ is conservative or it is invertible with non-singular inverse, then Cφ has single valued extension property.

Keywords

Composition Operator, Conservative, Decomposability, Decomposition Property (δ), Single Valued Extension Property.
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  • Local Spectral Properties of a Composition Operator on LP Spaces

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Authors

Shailesh Trivedi
Department of Mathematics, Banaras Hindu University Varanasi, 221005, India
Harish Chandra
Department of Mathematics and DST-CIMS, Banaras Hindu University, Varanasi, 221005, India

Abstract


In this paper, we discuss the decomposability and single valued extension property of composition operators Cφ on Lp(X)(1 ≤ p < ∞) spaces. We give a sufficient condition for non-decomposability of Cφ in terms of Radon-Nikodym derivative. Further, we prove that if φ is conservative or it is invertible with non-singular inverse, then Cφ has single valued extension property.

Keywords


Composition Operator, Conservative, Decomposability, Decomposition Property (δ), Single Valued Extension Property.