Operators which commute with convolution and their transforms

Commutators Which Commute with One Factor

Let A and B be n × n matrices, let C = ABA−1B−1 be the multiplicative commutator of A and B, and assume AC = CA. Olga Taussky (1961) examined the structure of A and B for the case where A and B are unitary. Marcus and Thompson (1966) generalized her results to the case where A and C are assumed normal. We look at this problem for general A, with particular attention to the cases where A is diag...

Continuityof Operators Intertwiningwith Convolution Operators

Let G be a locally compact abelian group, let m be a bounded complex-valued Borel measure on G; and let Tm be the corresponding convolution operator on LðGÞ: Let X be a Banach space and let S be a continuous linear operator on X : Then we show that every linear operator F : X ! LðGÞ such that FS 1⁄4 TmF is continuous if and only if the pair ðS;TmÞ has no critical eigenvalue. # 2002 Elsevier Sci...

Subordination and Super Ordination Results Involving Certain Convolution Operators

Hypercyclic Operators That Commute with the Bergman Backward Shift

The backward shift B on the Bergman space of the unit disc is known to be hypercyclic (meaning: it has a dense orbit). Here we ask: “Which operators that commute with B inherit its hypercyclicity?” We show that the problem reduces to the study of operators of the form φ(B) where φ is a holomorphic self-map of the unit disc that multiplies the Dirichlet space into itself, and that the question o...

Integral transforms, convolution products, and first variations

We establish the various relationships that exist among the integral transform Ᏺ α,β F , the convolution product (F * G) α , and the first variation δF for a class of functionals defined on K[0,T ], the space of complex-valued continuous functions on [0,T ] which vanish at zero. 1. Introduction and definitions. In a unifying paper [10], Lee defined an integral transform Ᏺ α,β of analytic functi...