Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols. (13th January 2021)

• Record Type: Journal Article
• Authors: Hernández-Eliseo, Yessica; Ramírez-Ortega, Josué; Hernández-Zamora, Francisco G.
• Other Names: Gheondea Aurelian Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-01-13
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/8855599
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We describe certain C ∗ -algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D 2 ⊂ ℂ 2 . Bounded measurable functions of the form c Im ζ 1, Im ζ 2 − ζ 1 2 are called nilpotent symbols. In this work, we consider symbols of the form a Im ζ 1 b Im ζ 2 − ζ 1 2, where both limits lim s → 0 + b s and lim s → + ∞ b s exist, and a s belongs to the set of piecewise continuous functions on ℝ ¯ = − ∞, + ∞ and having one-side limit values at each point of a finite set S ⊂ ℝ . We prove that the C ∗ -algebra generated by all Toeplitz operators T a b is isomorphic to C Π ¯, where Π ¯ = ℝ ¯ × ℝ ¯ + and ℝ ¯ + = 0, + ∞ .