2024/07/30 by Maria Helena Catelli de Carvalho, Carvalho, Maria, Udayan B. Darji +3
Computer Science · Decision Sciences · Mathematics · #37B65 #47B01 #47B37 #Approximation Theory and Sequence Spaces #Dynamical Systems (math.DS) #FOS: Mathematics #Fuzzy and Soft Set Theory #Primary 37C50 #Secondary 47B33 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2407.20890
openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We classify vast families of these shift operators, including the ones generated by orthogonal, diagonalizable, rotation or hyperbolic matrices. and this classification yields verifiable conditions which we use to construct concrete examples of shift operators with a variety of dynamical properties. As a consequence, we show that, for large classes of shift operators, generalized hyperbolicity is equivalent to the shadowing property.