Taylor Functional Calculus

Vladimir Müller ()
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Vladimir Müller: Mathematical Institute AV CR

Chapter 44 in Operator Theory, 2026, pp 1339-1374 from Springer

Abstract: Abstract The notion of spectrum of an operator is one of the central concepts of operator theory. It is closely connected with the existence of a functional calculus which provides important information about the structure of Banach space operators. The situation for commuting n-tuples of Banach space operators is much more complicated. There are many possible definitions of joint spectra. However, the joint spectrum introduced by J. L. Taylor has a distinguished property—there exists a functional calculus for functions analytic on a neighbourhood of this spectrum, and the Taylor spectrum is in some sense minimal (so the Taylor functional calculus is the richest). The present chapter gives a survey of basic properties of the Taylor spectrum and Taylor functional calculus.

Keywords: Taylor spectrum; Taylor functional calculus; Split spectrum; Primary: 47A60, 47A13; Secondary: 47A10 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_61

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