Results 191 to 200 of about 3,554 (232)

On Quasisimilarity for Toeplitz Operators

Canadian Mathematical Bulletin, 1985
AbstractIn this article we give a sufficient condition for quasisimilar analytic Toeplitz operators to be unitarily equivalent. We also use a result of Deddens and Wong to give a sufficient condition for an operator intertwining two analytic Toeplitz operators to intertwine their inner parts too.
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Toeplitz Operators

2023
AbstractThis chapter surveys Toeplitz operators Tφ : H2 → H2, Tφf = P + (φf), on the Hardy space H2, where φ ∈ L∞(T) and P+ is the orthogonal projection of L2(T) onto H2. We examine the matrix representations of these operators, their spectral properties, and a characterization of them related to the unilateral shift.
Stephan Ramon Garcia, Javad Mashreghi, William T. Ross   +2 more
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Properties of iteration of toeplitz operators with toeplitz preconditioners

BIT Numerical Mathematics, 1998
Toeplitz operators are preconditioned by approximations applied to the symbol (also known as generating function) of the operator. The preconditioned operator divides in two parts, a compact one and a perturbation. As a result, Krylov subspace methods exhibit superconvergence in initial iterations. Convergence estimates are given in terms of the symbol
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Rank of Truncated Toeplitz Operators

Complex Analysis and Operator Theory, 2016
A Toeplitz operator \(T_\phi\) with symbol \(\phi\in L^\infty\) is a map between Hardy spaces \(H^2\ni f\mapsto P(\phi f)\in H^2\), where \(P\) is the orthogonal projection onto \(H^2\). Recall that \(T_{\overline{f}g}=T_{\overline{f}}T_g\) for \(f,g\in H^\infty\).
Gu, Caixing, Kang, Dong-O
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Toeplitz Operators on the Fock Space

Integral Equations and Operator Theory, 2010
For positive parameter \(\alpha\), consider the measure \( d \lambda_{\alpha}(z)=\frac{\alpha}{\pi}e^{-\alpha|z|^{2}}dA(z) \) on the complex plane \(\mathbb C\), where \(dA(z)\) is the ordinary area measure. The Fock space \(F_{\alpha}^{2}\) is the subspace (with inherited norm) of all entire functions in \(L^{2}({\mathbb C},d\lambda_{\alpha})\).
Isralowitz, Josh, Zhu, Kehe
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Analytic Continuation of Toeplitz Operators

The Journal of Geometric Analysis, 2014
Let \(f(z)=\sum_\nu f_\nu z^\nu\) be a holomorphic function on the unit ball \({\mathbb B}^n\) in \({\mathbb C}^n\). For \(\alpha\in{\mathbb R}\), \textit{R.-H. Zhao} and \textit{K. Zhu} [Mém. Soc. Math. Fr., Nouv. Sér. 115, 1--103 (2008; Zbl 1176.32001)] considered \(\|f\|_{\alpha,\#}^2:=\sum_\nu\frac{\nu!}{|\nu|!}\frac{|f_\nu|^2}{(|\nu|+1)^{\alpha+n}}
Bommier-Hato, H., Engliš, M. (Miroslav), Youssfi, E.-H.   +2 more
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On Quasisimilarity for Analytic Toeplitz Operators

Canadian Mathematical Bulletin, 1988
AbstractLet f be a function in H∞. We show that if f is inner or if the commutant of the analytic Toeplitz operator Tf is equal to that of Tb for some finite Blaschke product b, then any analytic Toeplitz operator quasisimilar to Tf is unitarily equivalent to Tf.
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On Toeplitz Operators and Similarity

American Journal of Mathematics, 1978
Clark, Douglas N., Morrel, Judith H.
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When is a Function of a Toeplitz Operator Close to a Toeplitz Operator?

1989
In this paper we consider conditions under which the operator f(Tα) - T f·α belongs to the Schatten — von Heumann class Sp and in particular conditions when f(Tα) - T f·α is of trace class. Here Tα is a Toeplitz operator which is defined for bounded α on the Hardy class H2 by $$ {T_\varphi }f = {\mathbb{P}_ + }\varphi f $$ (1) , where P+ is ...
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Asymptotic Toeplitz Operators

Transactions of the American Mathematical Society, 1982
Barria, Jose, Halmos, P. R.
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