Toeplitz Operators whose Symbols Are Borel Measures. (8th April 2021)

• Record Type: Journal Article
• Authors: Park, Jaehui
• Other Names: Lu Chun Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-04-08
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/5599823
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we are concerned with Toeplitz operators whose symbols are complex Borel measures. When a complex Borel measure μ on the unit circle is given, we give a formal definition of a Toeplitz operator T μ with symbol μ, as an unbounded linear operator on the Hardy space. We then study various properties of T μ . Among them, there is a theorem that the domain of T μ is represented by a trichotomy. Also, it was shown that if the domain of T μ contains at least one polynomial, then T μ is densely defined. In addition, we give evidence for the conjecture that T μ with a singular measure μ reduces to a trivial linear operator.