Pure Subnormal Operators Have Cyclic Adjoints
نویسندگان
چکیده
منابع مشابه
Adjoints 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 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 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 کاملAdjoints 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 کاملNonlinear Hilbert Adjoints of Fliess Operators
Given a causal analytic nonlinear input-output system represented as a Chen-Fliess functional series, this paper investigates how to apply an existing notion of a nonlinear Hilbert adjoint operator to explicitly compute a corresponding adjoint operator. The method is demonstrated for the bilinear case.
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: 1999
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3367