Abstract
A method for estimating multiplicity of operators in terms of certain multilinear mappings is introduced. Several applications are given which include the following result: IfT is a completely non-unitary contraction on a complex Hilbert space, and\(T^n x_0 \mathop /\limits_ \to 0\) for some vectorx 0, then there exists a constant α>0, such that for every positive integern, the multiplicity of the operatorT n is not less thannα. This extends a result of B. Sz. Nagy and Foiaş [10].
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Atzmon, A. Multilinear mappings and estimates of multiplicity. Integr equ oper theory 10, 1–16 (1987). https://doi.org/10.1007/BF01199792
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DOI: https://doi.org/10.1007/BF01199792