BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture
Spectral characterization of shadowing for linear operators on Hilbert spaces
Wednesday 26th August 2026 at 13:00
Abstract. In this talk, we consider one of the fundamental notions in dynamical systems, the shadowing of invertible operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been in the focus of the research for a long time, spectral criteria for shadowing are available in the literature only for rather special classes of invertible operators. In this talk, we give a complete spectral characterization for the shadowing of an arbitrary invertible operator T on a complex Hilbert space. It is shown that T has the shadowing property if and only if its right spectrum is disjoint from the unit circle in the complex plane. As a consequence, the shadowing property for T is equivalent to the uniform expansivity of its adjoint operator.
At the department meeting room (2nd floor Z205), Žižkova 17.
THE LECTURE WILL BE GIVEN BY PROF. MIHÁLY PITUK,
Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary
The lecture is intended for all those interested in these problems.
doc. Mgr. Irena Hinterleitner, Ph.D.
Head of the Institute of Mathematics and Descriptive Geometry
