On linear chaos in function spaces

• Autorzy: Jimenez John M. , Markin Marat V.

Identyfikatory

DOI

10.1515/dema-2022-0008

• Języki publikacji: EN

Abstrakty

EN

We show that, in Lp(0,∞) ( 1≤p<∞ ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞) and describe the spectra of the weighted translations provided the underlying spaces are complex.

Słowa kluczowe

EN

hypercyclic vector; periodic point; hypercyclic operator; chaotic operator; spectrum

PL

wektory; punkt okresowy; operator; operatory hipercykliczne; widmo

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 119--135
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Jimenez John M.

• Department of Mathematics, De Anza College, 21250 Stevens Creek Blvd., Cupertino, CA 95014, USA

autor

Markin Marat V.

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

Bibliografia

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• [13] N. Dunford and J. T. Schwartz with the assistance of W. G. Bade and R. G. Bartle, Linear Operators. Part I: General Theory, Interscience Publishers, New York, 1958.
• [14] M. V. Markin, Elementary Operator Theory, De Gruyter Graduate, Walter de Gruyter GmbH, Berlin/Boston, 2020.
• [15] M. V. Markin, Real Analysis. Measure and Integration, De Gruyter Graduate, Walter de Gruyter GmbH, Berlin/Boston, 2019.
• [16] M. V. Markin, On sufficient and necessary conditions for linear hypercyclicity and chaos, arXiv:2106.14872.
• [17] M. V. Markin and E. S. Sichel, On the non-hypercyclicity of normal operators, their exponentials, and symmetric operators, Mathematics 7 (2019), no. 10, 903.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).