On the Berezin symbols and toeplitz operators
- Autores: Mübariz T. Karaev, Mehmet Gürdal
- Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 25, Nº 1, 2010, págs. 83-102
- Idioma: inglés
- Enlaces
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Resumen
The present paper mainly gives some new applications of Berezin symbols. In particular, the Berezin symbol is used in approximation problem for H1-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 T , which is the C¤-subalgebra of the operator algebra B(L2 a) generated by the Toeplitz operators fTg : g 2 H1g on the Bergman space L2 a(D). We characterize compactness of truncated Toeplitz operators A' = PKµT' j Kµ, ' 2 L1(T), in terms of Berezin symbols. The spectrum of model operators '(Mµ), ' 2 H1, is localized in terms of the so-called Berezin set by proving that ¾('(Mµ)) ½ closBer('(Mµ)). Reducing subspaces of n-tuple of invertible operators on the Hilbert space H are described.
