On the Commutant of Multiplication Operators with Analytic Rational Symbol
نویسندگان
چکیده
منابع مشابه
Adjoints 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 Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra
Let R D be the algebra generated in Sobolev space W22 D by the rational functions with poles outside the unit disk D. In this paper, we study the similarity invariant of the multiplication operators Mg in L R D , when g is univalent analytic on D or Mg is strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or ...
متن کاملMultiplication Operators on the Bergman Space via Analytic Continuation
ABSTRACT. In this paper, using the group-like property of local inverses of a finite Blaschke product φ, we will show that the largest C-algebra in the commutant of the multiplication operator Mφ by φ on the Bergman space is finite dimensional, and its dimension equals the number of connected components of the Riemann surface of φ ◦ φ over the unit disk. If the order of the Blaschke product φ i...
متن کاملIrreducible Multiplication Operators on Spaces of Analytic Functions
Mφ : H → H for φ ∈ H∞(Ω). We mention some known results in this area that serve as a motivation for the present paper. First, if H is the classical Hardy space of the unit disk D, and if φ is an inner function on D, then Mφ is a pure isometry and a shift operator on H , and so its reducing subspaces are in a one-to-one correspondence with the closed subspaces of H (φH). Therefore, the reducing ...
متن کاملPointwise multiplication operators on weighted Banach spaces of analytic functions
For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator Mφ, Mφ(f)=φf , on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Therefore we characterize when Mφ is Fredholm or is an isomorphism into. We study also cyclic phenomena of the adjoint map M ′ φ.
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: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2012
ISSN: 1370-1444
DOI: 10.36045/bbms/1331153416