.png){kind=icon}
.png){kind=icon}
Return
SJ-class operators and supercyclicity
.png){kind=icon}
PRE
AI
DOI：10.1080/03081087.2025.2596630.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper, we suggest a novel approach to linear dynamics based on the idea that supercyclicity can be localized. A nonzero vector x in a Banach space X is called an SJ-class vector for an operator T is an element of L(X)provided for every open neighborhood U(x)of x and every non empty open subset V of X and also for every N is an element of N, there exists a complexnumber lambda and an integer n>N such that lambda T-n(U-x)boolean AND V not equal 0. When an operator T has at least one SJ-class vector, it is called an operator of SJ-class. As a consequence, if T is a supercyclic operator, then it falls into the SJ-class. Aside from investigating theSJ-class operators, we provide some examples demonstrating that the SJ-class is an ewclass in L(X).We would like to emphasize that despite the fact that the non-separable Banach space l(infinity)(N)does not admits uper cyclic operators,it does admit operators of theSJ-class. Also, we provide a character-ization of theSJ-class operators on the Banach space X circle plus Cin terms of the J-class operators on the Banach space X.
Keywords:
Supercyclicity
J-class operators
SJ-class operators