Integral operators generated by weighted shift operators

1996 ◽  
Vol 59 (3) ◽  
pp. 321-323
Author(s):  
M. S. Bichegkuev
Keyword(s):  
Integral Operators ◽  
Weighted Shift ◽  
Shift Operators

CHAOS IN A CLASS OF NONCONSTANT WEIGHTED SHIFT OPERATORS

2013 ◽  
Vol 23 (01) ◽  
pp. 1350010 ◽  
Author(s):  
XINXING WU ◽  
PEIYONG ZHU
Keyword(s):  
Positive Integer ◽  
Linear Space ◽  
Normed Linear Space ◽  
Shift Operator ◽  
Weighted Shift ◽  
Constructive Proof ◽  
Sufficient Condition ◽  
Weighted Shift Operator ◽  
Shift Operators ◽  
Devaney Chaos

In this paper, chaos generated by a class of nonconstant weighted shift operators is studied. First, we prove that for the weighted shift operator Bμ : Σ(X) → Σ(X) defined by Bμ(x0, x1, …) = (μ(0)x1, μ(1)x2, …), where X is a normed linear space (not necessarily complete), weak mix, transitivity (hypercyclity) and Devaney chaos are all equivalent to separability of X and this property is preserved under iterations. Then we get that [Formula: see text] is distributionally chaotic and Li–Yorke sensitive for each positive integer N. Meanwhile, a sufficient condition ensuring that a point is k-scrambled for all integers k > 0 is obtained. By using these results, a simple example is given to show that Corollary 3.3 in [Fu & You, 2009] does not hold. Besides, it is proved that the constructive proof of Theorem 4.3 in [Fu & You, 2009] is not correct.

On reflexivity of hyponormal and weighted shift operators

2010 ◽  
Vol 30 (4) ◽  
pp. 1100-1104 ◽  
Author(s):  
M. Faghih Ahmadi ◽  
K. Hedayatian
Keyword(s):  
Weighted Shift ◽  
Shift Operators

Weighted Shift Operators Which are m-Isometries

2010 ◽  
Vol 68 (3) ◽  
pp. 301-312 ◽  
Author(s):  
Teresa Bermúdez ◽  
Antonio Martinón ◽  
Emilio Negrín
Keyword(s):  
Weighted Shift ◽  
Shift Operators

scholarly journals S-Numbers of Weighted Shift Operators on P-Summable Formal Entire Functions of M-Variables

2019 ◽  
Vol 15 (1) ◽  
pp. 79-85
Author(s):  
Nashat Faried ◽  
Z.A. Hassanain ◽  
H. Abd El Ghaffar ◽  
A. Lokman
Keyword(s):  
Entire Functions ◽  
Weighted Shift ◽  
Shift Operators

scholarly journals On linear operators and bases on Köthe spaces

2016 ◽  
Vol 1 (2) ◽  
pp. 617-624 ◽  
Author(s):  
M. Maldonado ◽  
J. Prada ◽  
M. J. Senosiain
Keyword(s):  
Analytic Functions ◽  
Generalized Derivation ◽  
Weighted Shift ◽  
Linear Operators ◽  
Shift Operators ◽  
Köthe Spaces ◽  
Unilateral Weighted Shift ◽  
Spaces Of Analytic Functions

AbstractWe make a survey of results published by the authors about the backward and forward unilateral weighted shift operators in Kóthe spaces, the so-called generalized derivation and integration operators, extending well-known results for spaces of analytic functions.

Sign in / Sign up

Export Citation Format

Share Document