J-Class Sequences of Linear Operators

Azimi, Mohammad Reza

doi:10.1007/s11785-017-0658-4

Cited by 2 publications

(1 citation statement)

References 19 publications

(20 reference statements)

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“…Proof See Lemma 2.6 in [2] for parts (a) and (b). If U has a bounded inverse, then for z ∈ J(T, U m x) , there exists a strictly increasing sequence of positive integers (k n ) n and a sequence (u n ) n in X such that u n → U m x and T kn u n → z.…”

Section: Lemma 23mentioning

confidence: 99%

On the J -reflexive operators

Hosseini¹,

Yousefi²

2018

Turk J Math

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A bounded linear operator T on a Banach space X is J-reflexive if every bounded operator on X that leaves invariant the sets J(T, x) for all x is contained in the closure of orb(T) in the strong operator topology. We discuss some properties of J-reflexive operators. We also give and prove some necessary and sufficient conditions under which an operator is J-reflexive. We show that isomorphisms preserve J-reflexivity and some examples are considered. Finally, we extend the J-reflexive property in terms of subsets.

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Section: Lemma 23mentioning

confidence: 99%

On the J -reflexive operators

Hosseini¹,

Yousefi²

2018

Turk J Math

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Jℱ-Class Weighted Backward Shifts

Yin

2018

Int. J. Bifurcation Chaos

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In this article [Formula: see text]-class operators are introduced and some basic properties of [Formula: see text]-vectors are given. The [Formula: see text]-class operators include the [Formula: see text]-class operators and [Formula: see text]-class operators introduced by Costakis and Manoussos in 2008. This class also includes the [Formula: see text]-class and [Formula: see text]-class operators defined by Zhang [2012]. Furthermore, for the unilateral weighted backward shifts on a Fréchet sequence space, we establish a criterion under which the shift operators belong to the [Formula: see text]-class. From the criterion it is easy to obtain the existing criteria of hypercyclic backward shifts and of the topological mixing backward shifts. The obtained criterion also reveals the characteristic of [Formula: see text]-class shift operators by the recurrence property. Meanwhile, we obtain infinite topological entropy when the shifts have stronger recurrence property, which generalizes the related results by Brian et al. in 2017.

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J-Class Sequences of Linear Operators

Cited by 2 publications

References 19 publications

On the J -reflexive operators

On the J -reflexive operators

Jℱ-Class Weighted Backward Shifts

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