The commutant of an analytic Toeplitz operator
نویسندگان
چکیده
منابع مشابه
On a weighted Toeplitz operator and its commutant
We study the structure of a class of weighted Toeplitz operators and obtain a description of the commutant of each operator in this class. We make some progress towards proving that the only operator in the commutant which is not a scalar multiple of the identity operator and which commutes with a nonzero compact operator is zero. The proof of the main statement relies on a conjecture which is ...
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Unlike Toeplitz operators on H, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several e...
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A slant weighted Toeplitz operator Aφ is an operator on L(β) defined as Aφ = WMφ where Mφ is the weighted multiplication operator and W is an operator on L(β) given by We2n = βn β2n en, {en}n∈Z being the orthonormal basis. In this paper, we generalise Aφ to the k-th order slant weighted Toeplitz operator Uφ and study its properties. Keywords—Slant weighted Toeplitz operator, weighted multiplica...
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Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in ...
متن کاملOn 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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1978
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1978-0482347-9