Weighted translation operators and linear extensions of dynamical systems. (English. Russian original) Zbl 0752.47011

Latushkin, Yu. D.; Stëpin, A. M.

Russ. Math. Surv. 46, No. 2, 95-165 (1991); translation from Usp. Mat. Nauk 46, No. 2(278), 85-143 (1991).

The survey is devoted to the investigation of the connection between the theory of functional operators with shift and linear extensions of dynamical systems.
Contents: §1 Semi-groups of weighted shift operators. §2 Algebras of weighted shift operators. §3 Weighted shift operators and spectral theory of linear extensions. §4 Weighted shift operators and multiplicative ergodic theorems.

Reviewer: N.K.Karapetyants (Rostov-na-Donu)

MSC:

47B37	Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A35	Ergodic theory of linear operators

Keywords:

functional operators; shift; linear extension of dynamical systems; weighted shift operators; spectral theory; multiplicative ergodic theorems