unilateral weighted shift
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Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 212
Author(s):  
Chunji Li ◽  
Cheon Ryoo

Let 1 < a < b < c < d and α ^ 5 : = 1 , a , b , c , d ∧ be a weighted sequence that is recursively generated by five weights 1 , a , b , c , d . In this paper, we give sufficient conditions for the positive quadratic hyponormalities of W α x and W α y , x , with α x : x , α ^ 5 and α y , x : y , x , α ^ 5 .


2017 ◽  
Vol 39 (4) ◽  
pp. 898-924 ◽  
Author(s):  
ROMUALD ERNST ◽  
AUGUSTIN MOUZE

We give a quantitative interpretation of the frequent hypercyclicity criterion. Actually we show that an operator which satisfies the frequent hypercyclicity criterion is necessarily $A$-frequently hypercyclic, where $A$ refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the ‘frequency’ measured by the frequent hypercyclicity criterion. Moreover, we construct an example of a unilateral weighted shift which is frequently hypercyclic but not $A$-frequently hypercyclic on a particular scale.


2016 ◽  
Vol 1 (2) ◽  
pp. 617-624 ◽  
Author(s):  
M. Maldonado ◽  
J. Prada ◽  
M. J. Senosiain

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.


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