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Convolution Equations and Singular Integral Operators pp 157–184Cite as

On a Local Principle and Algebras Generated by Toeplitz Matrices

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 206))

Abstract

The main topic of the present paper is the study of some Banach algebras of bounded linear operators acting in the spaces ℓ p (1 < p < ∞). Generators of these algebras are defined by Toeplitz matrices constructed from the Fourier coefficients of functions having finite limits from the left and from the right at each point.

The paper was originally published as И.Ц. Гохберг, Н.Я. Крупник, Об одном локалном принципе и алгебрах, порождэнных тэплицевыми матрицами, An. Şti. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 19 (1973), 43-71. MR0399923 (53 #3763b), Zbl 0437.47019.

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References

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Authors
  1. Israel Gohberg
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  2. Nahum Krupnik
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Leonid Lerer

  2. Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA

    Vadim Olshevsky

  3. Department of Mathematics, College of William & Mary, Williamsburg, VA, 23187-8795, USA

    Ilya M. Spitkovsky

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Gohberg, I., Krupnik, N. (2010). On a Local Principle and Algebras Generated by Toeplitz Matrices. In: Lerer, L., Olshevsky, V., Spitkovsky, I.M. (eds) Convolution Equations and Singular Integral Operators. Operator Theory: Advances and Applications, vol 206. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8956-7_11

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