Abstract
Let S be the smallest closed subalgebra of operators on L 2 H (ℤ) which contains all one-dimensional singular integral operators with operator-valued piecewise quasi-continuous coefficients. We consider the stability problem for operator sequences belonging to the algebra which is generated by the sequences of finite sections of operators in S. The investigations are strongly based on C*-algebra methods, and we prove that a sequence belonging to that algebra is stable if and only if a certain well-defined collection of operators consists only of invertible ones.
Research supported by a DFG Heisenberg grant
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© 1996 Birkhäuser Verlag, Basel/Switzerland
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Ehrhardt, T., Roch, S., Silbermann, B. (1996). Finite Section Method for singular integrals with operator-valued PQC-coefficients. In: Böttcher, A., Gohberg, I. (eds) Singular Integral Operators and Related Topics. Operator Theory Advances and Applications, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9040-3_7
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DOI: https://doi.org/10.1007/978-3-0348-9040-3_7
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