Operators Whose Conjugation Orbits Satisfy Polynomial Growth Conditions

2019/04/10 by Heybetkulu Mustafayev, Mustafayev, Heybetkulu
Mathematics · #30D20 #47A10 #47A11 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1904.05125

openalex publication_date 2019/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a bounded linear operator on a complex Banach space X. For a given α≥ 0, we consider the class D_A^α( ℝ ) of all bounded linear operators T on X for which there exists a constant C_T>0, such that \Vert e^tATe^-tA\Vert ≤ C_T( 1+\vert t\vert ) ^α, \text ∀ t∈ ℝ We present complete description of the class D_A^α( ℝ ) in the case when the spectrum of A consists of one point. These results are linked to the decomposability of A. Some estimates for the norm of the commutator AT-TA are obtained in the case 0≤ α<1.

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