Adjoints of rationally induced composition operators
نویسندگان
چکیده
منابع مشابه
Adjoints of rationally induced composition operators
We give an elementary proof of a formula recently obtained by Hammond, Moorhouse, and Robbins for the adjoint of a rationally induced composition operator on the Hardy space H2 [Christopher Hammond, Jennifer Moorhouse, and Marian E. Robbins, Adjoints of composition operators with rational symbol, J. Math. Anal. App., to appear]. We discuss some variants and implications of this formula, and use...
متن کاملAdjoints of composition operators with rational symbol
Building on techniques developed by Cowen and Gallardo-Gutiérrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H2. We consider some specific examples, comparing our formula with several results that were previously known. 1. Preliminaries Let D denote the open unit disk in the complex plane. The Hardy space H is the Hilbert ...
متن کاملA New Class of Operators and a Description of Adjoints of Composition Operators
Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toep...
متن کاملAdjoints of Elliptic Cone Operators
We study the adjointness problem for the closed extensions of a general b-elliptic operator A ∈ x Diffmb (M ;E), ν > 0, initially defined as an unbounded operator A : C∞ c (M ;E) ⊂ x L b (M ;E) → xL b (M ;E), μ ∈ R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.
متن کاملAdjoints and Self-Adjoint Operators
Let V and W be real or complex finite dimensional vector spaces with inner products 〈·, ·〉V and 〈·, ·〉W , respectively. Let L : V → W be linear. If there is a transformation L∗ : W → V for which 〈Lv,w〉W = 〈v, Lw〉V (1) holds for every pair of vectors v ∈ V and w in W , then L∗ is said to be the adjoint of L. Some of the properties of L∗ are listed below. Proposition 1.1. Let L : V →W be linear. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2008
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2008.07.002