Abstract
In this chapter we develop the theory of Laurent and Toeplitz operators for the case when the underlying space is ℓ p with 1 ≤ p < ∞. To keep the presentation as simple as possible we have chosen a special class of symbols, namely those that are analytic in an annulus around the unit circle. For this class of symbols the results are independent of p. We prove the theorems about left and right invertibility and derive the Fredholm properties. Also, the convergence of the finite section method is analyzed. In the proofs factorization is used systematically. The chapter also contains extensions of the theory to pair operators and to a simple class of singular integral operators on the unit circle.
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© 2003 Springer Basel AG
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Gohberg, I., Goldberg, S., Kaashoek, M.A. (2003). Toeplitz and Singular Integral Operators. In: Basic Classes of Linear Operators. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7980-4_16
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DOI: https://doi.org/10.1007/978-3-0348-7980-4_16
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6930-9
Online ISBN: 978-3-0348-7980-4
eBook Packages: Springer Book Archive