Some classes of operators with symbol on the Lipschitz space of a tree |
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Authors: | Flavia?Colonna Email author" target="_blank">Rubén?A?Martínez-Avenda?oEmail author |
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Institution: | 1.Department of Mathematical Sciences,George Mason University,Fairfax,USA;2.Centro de Investigación en Matemáticas,Universidad Autónoma del Estado de Hidalgo,Pachuca,Mexico |
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Abstract: | In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum. |
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