$C^*$-algebras generated by multiplication operators and composition operators with 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 ...
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Let φ be a linear-fractional self-map of the open unit disk D, not an automorphism, such that φ(ζ) = η for two distinct points ζ, η in the unit circle ∂D. We consider the question of which composition operators lie in C∗(Cφ,K), the unital C∗-algebra generated by the composition operator Cφ and the ideal K of compact operators, acting on the Hardy space H. This necessitates a companion study of ...
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If φ is an analytic map of the unit diskD into itself, the composition operator Cφ on the Hardy space H (D) is defined by Cφ(f) = f ◦ φ. For a certain class of composition operators with multivalent symbol φ, we identify a subspace of H(D) on which C∗ φ behaves like a weighted shift. We reproduce the description of the spectrum found in [5] and show for this class of composition operators that ...
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ژورنال
عنوان ژورنال: Journal of Operator Theory
سال: 2016
ISSN: 0379-4024,1841-7744
DOI: 10.7900/jot.2015mar03.2085