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.
KeywordsBanach Space Banach Algebra Functional Calculus Spectral System Koszul Complex
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