2021/09/10 by Evgeniy Pustylnik, Pustylnik, Evgeniy
Computer Science · Mathematics · #46B70 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2109.05968
openalex publication_date 2021/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. No analytical presentation of operators, spaces and interpolation functor is required. We use only some little-known properties of compact sets and various facts about bases and basic sequences (with detailed references to the monograph "Bases in Banach spaces", Vol. I-II by I.M. Singer). Therefore the results are applicable to arbitrary spaces and any interpolation functor, including the complex method. The "two-sided" compactness is also mentioned at the end of this paper as a mere corollary.