The Journal of the Indian Mathematical Society

Shailesh Trivedi ¹, Harish Chandra ²

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

Abstract

In this paper, we discuss the decomposability and single valued extension property of composition operators Cφ on L^p(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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Vijay Kumar Srivastava ¹, Harish Chandra ¹

Affiliations
1 Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, IN

Abstract

In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on l^p(1 ≤ p < ∞). We prove that no composition operator is hypercyclic on l^p. Further, we also prove that C_Φ : l^p → l^p is supercyclic if and only if Φ is injective and Φⁿ has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.

Keywords

Hypercyclicity, Supercyclicity, Cyclicity, Composition Operator on lp.

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