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Symbol analysis

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Analysis of Toeplitz Operators

Part of the book series: Springer Monographs in Mathematics ((SMM))

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Abstract

Let F be a closed subset of X = M(L∞) and let a ∈ L ∞ N×N . The matrix function a is called analytically sectorial on F if there exist a real number ε > 0 and two invertible matrices b, c ∈ ℂ N×N such that Re (ba(x) c) ≧ ε for all x ∈ F, that is,

$$\operatorname{Re} \left( {ba\left( x \right)cz,z} \right) \geqslant \varepsilon {\left\| z \right\|^2}\quad \forall x \in F\forall z \in {{\Bbb C}_N},$$

and a is said to be geometrically sectorial on F if

$$conv\;\alpha \left( F \right) \subset G{{\Bbb C}_{N \times N}},$$

that is, if each matrix in the closed convex hull of a(F) is invertible.

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Notes and comments

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Authors and Affiliations

  1. Sektion Mathematik, Wissenschaftsbereich Analysis, Technische Universität Chemnitz, PSF 964, DDR-9010, Chemnitz, Germany

    Dr. rer. nat. Albrecht Böttcher & Prof. Dr. sc. nat. Bernd Silbermann

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  1. Dr. rer. nat. Albrecht Böttcher
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  2. Prof. Dr. sc. nat. Bernd Silbermann
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© 1990 Springer-Verlag Berlin Heidelberg

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Böttcher, A., Silbermann, B. (1990). Symbol analysis. In: Analysis of Toeplitz Operators. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02652-6_3

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  • DOI: https://doi.org/10.1007/978-3-662-02652-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-02654-0

  • Online ISBN: 978-3-662-02652-6

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