Weighted backward shift operators with invariant distributionally scrambled subsets

2017 ◽  
Vol 8 (2) ◽  
pp. 199-210 ◽  
Author(s):  
Xinxing Wu ◽  
Lidong Wang ◽  
Guanrong Chen
Keyword(s):  
Shift Operators ◽  
Backward Shift

scholarly journals Algebrability of the set of hypercyclic vectors for backward shift operators

2020 ◽  
Vol 366 ◽  
pp. 107082 ◽  
Author(s):  
Javier Falcó ◽  
Karl-G. Grosse-Erdmann
Keyword(s):  
Shift Operators ◽  
Hypercyclic Vectors ◽  
Backward Shift

CHAOS FOR BACKWARD SHIFT OPERATORS

2002 ◽  
Vol 12 (08) ◽  
pp. 1703-1715 ◽  
Author(s):  
F. MARTÍNEZ-GIMÉNEZ ◽  
A. PERIS
Keyword(s):  
Dynamical Systems ◽  
Differential Operator ◽  
Applied Mathematics ◽  
Linear Dynamical Systems ◽  
Infinite Dimensional ◽  
Shift Operators ◽  
Rich Variety ◽  
Backward Shift ◽  
Backward Shifts ◽  
Spaces Of Analytic Functions

Backward shift operators provide a general class of linear dynamical systems on infinite dimensional spaces. Despite linearity, chaos is a phenomenon that occurs within this context. In this paper we give characterizations for chaos in the sense of Auslander and Yorke [1980] and in the sense of Devaney [1989] of weighted backward shift operators and perturbations of the identity by backward shifts on a wide class of sequence spaces. We cover and unify a rich variety of known examples in different branches of applied mathematics. Moreover, we give new examples of chaotic backward shift operators. In particular we prove that the differential operator I + D is Auslander–Yorke chaotic on the most usual spaces of analytic functions.

On Shift Operators

1988 ◽  
Vol 31 (1) ◽  
pp. 85-94 ◽  
Author(s):  
J. R. Holub
Keyword(s):  
Banach Space ◽  
Separable Hilbert Space ◽  
Shift Operator ◽  
Continuous Functions ◽  
Usual Definition ◽  
Shift Operators ◽  
Spaces Of Continuous Functions ◽  
Backward Shift ◽  
The Common ◽  
Definition Of

AbstractA definition of an isometric shift operator on a Banach space is given which extends the usual definition of a shift operator on a separable Hilbert space. It is shown that there is no such shift on many of the common Banach spaces of continuous functions. The associated ideas of a semi-shift and a backward shift are also introduced and studied in the case of continuous function spaces.

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