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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$.
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Temel Bulgular & Veri:The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1].
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Sonuç & Katkı:We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Orbit · hypercyclic sets of operators · hypercyclic Operators
Abstract
Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$. The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1]. In this work, we introduce the notion of hypercyclic criterion for a subset of $\mathcal{B}(X)$. We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
AMOUCH, M., BENCHIHEB, O. (2019). On linear dynamics of sets of operators. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 402–411. https://ajindex.com/articles/218058