Volterra type operators on minimal Mobius invariant space
Huayou Xie, Junming Liu, Saminathan Ponnusamy
TL;DR
This paper investigates properties of Volterra type operators on the minimal Mobius invariant Besov space, including boundedness, algebra membership, norm estimates, and spectral characterization.
Contribution
It provides new insights into the operator-theoretic behavior of Volterra type operators on the minimal Mobius invariant space, including spectral and norm results.
Findings
Volterra operators are bounded on the space.
They belong to the Deddens algebra of composition operators.
Complete spectral characterization is achieved.
Abstract
In this note, we mainly study operator-theoretic properties on Besov space on the unit disc. This space is the minimal Mobius invariant space. Firstly, we consider the boundedness of Volterra type operators. Secondly, we prove that Volterra type operators belong to the Deddens algebra of composition operator. Thirdly, we obtain estimates for the essential norm of Volterra type operators. Finally, we give a complete characterization of spectrum of Volterra type operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Differential Equations and Boundary Problems · Algebraic and Geometric Analysis