Topological Transitivity of Shift Similar Operators on Nonseparable Hilbert Spaces

Author:

Zagorodnyuk Andriy1ORCID,Novosad Zoriana2ORCID

Affiliation:

1. Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., Ivano-Frankivsk 76018, Ukraine

2. Lviv University of Trade and Economics, 10 Tuhan-Baranovsky Str., Lviv 79005, Ukraine

Abstract

In this paper, we investigate topological transitivity of operators on nonseparable Hilbert spaces which are similar to backward weighted shifts. In particular, we show that abstract differential operators and dual operators to operators of multiplication in graded Hilbert spaces are similar to backward weighted shift operators.

Funder

National Research Foundation of Ukraine

Publisher

Hindawi Limited

Subject

Analysis

Reference18 articles.

1. Dynamics of Linear Operators

2. Démonstration d’un théorème élémentaire sur les fonctions entières;G. D. Birkhoff;C. R. Acad. Sci. Paris,1929

3. Sequences of derivatives and normal families

4. The range of operators on von Neumann algebras

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