On the essential commutant of the Toeplitz algebra on the Bergman space
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چکیده
منابع مشابه
On the Essential Commutant of the Toeplitz Algebra on the Bergman Space
Let T be the C∗-algebra generated by the Toeplitz operators {Tf : f ∈ L∞(B, dv)} on the Bergman space of the unit ball. We show that the essential commutant of T equals {Tg : g ∈ VObdd}+K, where VObdd is the collection of bounded functions of vanishing oscillation on B and K denotes the collection of compact operators on La(B, dv).
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In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero. 2002 Elsevier Science (USA). All rights reserved.
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Let Tf denote the Toeplitz operator with symbol function f on the Bergman space La(B, dv) of the unit ball in C . It is a natural problem in the theory of Toeplitz operators to determine the norm closure of the set {Tf : f ∈ L∞(B, dv)} in B(La(B, dv)). We show that the norm closure of {Tf : f ∈ L∞(B, dv)} actually coincides with the Toeplitz algebra T , i.e., the C∗-algebra generated by {Tf : f...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2017
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2017.01.020