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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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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.   +2 more
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On Toeplitz Operators with Biharmonic Symbols

Bulletin of the Malaysian Mathematical Sciences Society, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yousef, A., Al-Naimi, R.
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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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Essentially commuting Toeplitz operators

Pacific Journal of Mathematics, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gorkin, Pamela, Zheng, Dechao
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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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Toeplitz operators on l p

1990
Some questions for Toeplitz operators on H p have already been answered in the preceding chapters. In particular, we settled the Fredholm theory for the operators in algℒ (H N p ) T(C N × N +H N × N ∞ ). Also notice the localization result stated in Theorem 2.96. However, many questions still remain open and it is only a small number of them which will
Albrecht Böttcher, Bernd Silbermann
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Toeplitz Operators and Toeplitz C*-Algebras

1996
In this chapter we develop a structure theory for multi-variable Toeplitz operators, using the Toeplitz C*-algebra generated by these operators and its representation theory.
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On Toeplitz Operators and Similarity

American Journal of Mathematics, 1978
Clark, Douglas N., Morrel, Judith H.
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Asymptotic Toeplitz Operators

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