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Chandra, Harish
- Local Spectral Properties of a Composition Operator on LP Spaces
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Authors
Affiliations
1 Department of Mathematics, Banaras Hindu University Varanasi, 221005, IN
2 Department of Mathematics and DST-CIMS, Banaras Hindu University, Varanasi, 221005, IN
1 Department of Mathematics, Banaras Hindu University Varanasi, 221005, IN
2 Department of Mathematics and DST-CIMS, Banaras Hindu University, Varanasi, 221005, IN
Source
The Journal of the Indian Mathematical Society, Vol 82, No 3-4 (2015), Pagination: 219-226Abstract
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.- Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on Lp Spaces
Abstract Views :359 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, IN
1 Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 187-198Abstract
In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on lp(1 ≤ p < ∞). We prove that no composition operator is hypercyclic on lp. Further, we also prove that CΦ : lp → lp 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.References
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