Abstract
In this chapter we introduce and study another important spectral system for commuting operators — the Taylor spectrum. Although the definition of the Taylor spectrum is rather complicated, the Taylor spectrum has a distinguished property among other spectral systems, namely the existence of the functional calculus for functions analytic on a neighbourhood of the Taylor spectrum. From this reason many experts consider the Taylor spectrum to be the proper generalization of the ordinary spectrum for single operators.
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© 2007 Birkhäuser Verlag AG, P.O. Box 133, CH-4010 Basel, Switzerland
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(2007). Taylor Spectrum. In: Spectral Theory of Linear Operators. Operator Theory: Advances and Applications, vol 139. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8265-0_4
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DOI: https://doi.org/10.1007/978-3-7643-8265-0_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8264-3
Online ISBN: 978-3-7643-8265-0
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