quasinilpotent operators
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2019 ◽  
Vol 245 (3) ◽  
pp. 289-296
Author(s):  
Il Bong Jung ◽  
Eungil Ko ◽  
Carl Pearcy

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4717-4720
Author(s):  
Junfeng Liu

Let X be a Banach space with an unconditional basis, and let C ? {0} be a collection of continuous linear operators with modulus on X that is finitely modulus-quasinilpotent at a non-zero positive vector. Then C and its right modulus sub-commutant C'm have a common non-trivial invariant closed ideal.


2017 ◽  
Vol 60 (2) ◽  
pp. 364-371 ◽  
Author(s):  
Ciprian Preda

AbstractLet S := {S(t)}t≥0 be a C0-semigroup of quasinilpotent operators (i.e., σ(S(t)) = {0} for eacht> 0). In dynamical systems theory the above quasinilpotency property is equivalent to a very strong concept of stability for the solutions of autonomous systems. This concept is frequently called superstability and weakens the classical ûnite time extinction property (roughly speaking, disappearing solutions). We show that under some assumptions, the quasinilpotency, or equivalently, the superstability property of a C0-semigroup is preserved under the perturbations of its infinitesimal generator.


2017 ◽  
Vol 112 ◽  
pp. 281-306
Author(s):  
Jarmo Malinen ◽  
Olavi Nevanlinna ◽  
Jaroslav Zemánek

2016 ◽  
Vol 284 (3-4) ◽  
pp. 781-790
Author(s):  
Eva A. Gallardo-Gutiérrez ◽  
Jonathan R. Partington ◽  
Daniel J. Rodríguez

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