Please use this identifier to cite or link to this item:
Title: On the Berezin symbols and Toeplitz operators
Authors: Karaev, Mübariz T.
Gürdal, Mehmet
Keywords: Símbolo de Berezin;Espacio de Hardy;Espacio de Bergman;Operador de Toeplitz;Truncado;Función interna;Berezin symbol;Hardy space;Bergman space;Toeplitz operator;Truncated Toeplitz operator;Inner function
Issue Date: 2010
Publisher: Universidad de Extremadura, Servicio de Publicaciones
Abstract: The present paper mainly gives some new applications of Berezin symbols. In particular, the Berezin symbol is used in approximation problem for 𝐻∞-functions. We study also asymptotic multiplicativity of the Berezin symbols. Moreover, we study the solvability of some Riccati operator equations of the form XAX + XB- CX = D on the Toeplitz algebra 𝜏 , which is the C*-subalgebra of the operator algebra 𝛣(L² ₐ) generated by the Toeplitz operators {T𝑔 : 𝑔 ϵ H∞} on the Bergman space (L² ₐ) (𝔻). We characterizecompactness of truncated Toeplitz operators Aᵩ = PₖɵT ǁ, Kɵ, 𝜑ϵL∞(𝕋), in terms of Berezin symbols. The spectrum of model operators 𝜑(Mɵ), 𝜑 ϵ H∞, is localized in terms of the so-called Berezin set by proving that σ(𝜑(Mѳ)) ⊂ closBer(𝜑(Mѳ)). Reducing subspaces of n-tuple of invertible operators on the Hilbert space H are described.
ISSN: 0213-8743
Appears in Collections:Extracta Mathematicae Vol. 25, nº 1 (2010)

Files in This Item:
File Description SizeFormat 
0213-8743_25_1_83.pdf231,74 kBAdobe PDFView/Open

This item is licensed under a Creative Commons License Creative Commons