Spectral mapping theorems for essential spectra and regularized functional calculi

2022/06/28 by Jesús Oliva-Maza, Oliva-Maza, Jesús
Mathematics · #47A10 #47A53 #47A60 #47B12 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.13955

openalex publication_date 2022/06/28 · openalex created_date 2022/07/01 · openalex updated_date 2026/07/28

Abstract

Gramsch and Lay [10] gave spectral mapping theorems for the Dunford-Taylor calculus of a closed linear operator T, \widetildeσ_i(f(T)) = f(\widetildeσ_i(T)), for several extended essential spectra \widetildeσ_i. In this work, we extend such theorems for the natural functional calculus introduced by Haase [12,13]. We use the model case of bisectorial operators. The proofs presented here are generic, and are valid for similar functional calculus.

Related

• The Functional Calculus Approach to the Spectral Theorem
• Spectrum as the Support of Functional Calculus
• The essential spectrum of Schrodinger, Jacobi, and CMV operators
• A direct approach to the S-functional calculus for closed operators
• Spectral mapping theorem and the Taylor spectrum