Asymptotic Toeplitz and Hankel operators on the Bergman space

Namita Das ()
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Namita Das: Utkal University

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 2, 379-400

Abstract: Abstract In this paper the concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense.

Keywords: Toeplitz operators; Hankel operators; Bergman space; Hardy space; Bergman shift operator (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0023-z

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