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http://hdl.handle.net/10662/13340
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. |
URI: | http://hdl.handle.net/10662/13340 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 25, nº 1 (2010) |
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