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On linear chaos in function spaces

Jimenez John M., Markin Marat V.

Demonstratio Mathematica

2022

Vol. 55, nr 1

119--135

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.

Generalized sturm separation theorem

Przeworska-Rolewicz D.

Demonstratio Mathematica

2003

Vol. 36, nr 3

735--746

True shifts for right invertible operators has been examined in several papers in various aspects (cf. PR[4], PR[5]). A generalization of Sturm separation theorem was given in PR[2] in the case when a right invertible operator under consideration had the one-dimensional kernel. Following the preprint [6], it is shown that the Sturm theorem holds without any assumption about the dimension of that kernel. In the last section of the present paper there are considered the multiplicative symbols in Leibniz algebras.

True shifts revisited

Przeworska-Rolewicz D.

Demonstratio Mathematica

2001

Vol. 34, nr 1

111-122