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Properties of the slant weighted Toeplitz operator. (English) Zbl 1219.47046
Summary: If $\beta = \langle\beta\rangle_{n\in \bbfZ}$ is a sequence of positive numbers, then a slant weighted Toeplitz operator $A_\varphi$ is an operator on $L^2(\beta)$ defined as $A_\varphi = W M_\varphi$, where $M_\varphi $ is the multiplication operator on $L^2(\beta )$. When the sequence $\beta \equiv 1$, this operator reduces to the ordinary slant Toeplitz operator given by {\it M. C. Ho} [Indiana Univ. Math. J. 45, No. 3, 843--862 (1996; Zbl 0880.47016)]. In this paper, we study some algebraic properties of a slant weighted Toeplitz operator. We also obtain its matrix characterization and discuss the adjoint of this operator.
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B35Toeplitz operators, Hankel operators, Wiener-Hopf operators
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