Abstract
We give in this paper some asymptotic von Neumann inequalities for power bounded operators in the class \(C_\rho \cap C_{1,} .\) and some spacial von Neumann inequalities associated with non zero elements of the point spectrum, when it is non void, of generalized Toeplitz operators. Introducing perturbed kernel, we consider classes C R which extend the classical classes Cρ. We give results about absolute continuity with respect to the Haar measure for operators in class \(C_R \cap C_{1,} .\). This allows us to give new results on cyclic vectors for such operators and provides invariant subspaces for their powers. Relationships between cyclic vectors for T and T* involving generalized Toeplitz operators are given and the commutativity of {T}’, the commutant of T is discussed.
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© 2004 Birkhäuser Verlag Basel/Switzerland
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Cassier, G., Mahzouli, H., Zerouali, E. (2004). Generalized Toeplitz Operators and Cyclic Vectors. In: Gaşpar, D., Timotin, D., Zsidó, L., Gohberg, I., Vasilescu, FH. (eds) Recent Advances in Operator Theory, Operator Algebras, and their Applications. Operator Theory: Advances and Applications, vol 153. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7314-8_6
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DOI: https://doi.org/10.1007/3-7643-7314-8_6
Publisher Name: Birkhäuser Basel
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