On the non-hypercyclicity of scalar type spectral operators and collections of their exponentials

• Autorzy: Markin Marat V.

Identyfikatory

DOI

10.1515/dema-2020-0030

• Języki publikacji: EN

Abstrakty

EN

Generalizing the case of a normal operator in a complex Hilbert space, we give a straightforward proof of the non-hypercyclicity of a scalar type spectral operator A in a complex Banach space as well as of the collection {etA}t≥0 of its exponentials, which, under a certain condition on the spectrum of the operator A, coincides with the C0-semigroup generated by A. The spectrum of A lying on the imaginary axis, we also show that non-hypercyclic is the strongly continuous group {etA}t∈R of bounded linear operators generated by A. From the general results, we infer that, in the complex Hilbert space L2(R), the anti-self-adjoint differentiation operator A≔ddx with the domain D(A)≔W12(R) is non-hypercyclic and so is the left-translation strongly continuous unitary operator group generated by A.

Słowa kluczowe

EN

hypercyclicity; scalar-type spectral operators; normal operator; Co-semigroup; strongly continuous operator group

PL

hipercykliczność; operator naturalny; półgrupa Co; mocno ciągłe półgrupy; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 352--359
• Opis fizyczny: Bibliogr. 32 poz.

Twórcy

autor

Markin Marat V.

• Department of Mathematics, California State University, Fresno, 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA

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