On the Non-Hypercyclicity of Normal Operators, Their Exponentials, and Symmetric Operators
Copyright policy )On the Non-Hypercyclicity of Normal Operators, Their Exponentials, and Symmetric Operators
We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator A in a complex Hilbert space as well as of the collection e t A t ≥ 0 of its exponentials, which, under a certain condition on the spectrum of A, coincides with the C 0 -semigroup generated by it. We also establish non-hypercyclicity for symmetric operators.
- California State University, Fresno United States
- California State University, San Marcos United States
hypercyclicity, <i>c</i><sub>0</sub>-semigroup, Primary 47A16, 47B15, Secondary 47D06, 47D60, 34G10, <i>C</i><sub>0</sub>-semigroup, scalar type spectral operator, normal operator, Functional Analysis (math.FA), Mathematics - Functional Analysis, QA1-939, FOS: Mathematics, Mathematics
hypercyclicity, <i>c</i><sub>0</sub>-semigroup, Primary 47A16, 47B15, Secondary 47D06, 47D60, 34G10, <i>C</i><sub>0</sub>-semigroup, scalar type spectral operator, normal operator, Functional Analysis (math.FA), Mathematics - Functional Analysis, QA1-939, FOS: Mathematics, Mathematics
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