Abstract
In the present chapter we introduce the notion of the multiplicative operator integral in a separable Hilbert space H. By virtue of the multiplicative operator integral, we derive spectral representations for resolvents of various classes of P-triangular operators. These representations are generalizations of the classical spectral representation for the resolvent of a normal operator. If the maximal resolution of the identity is discrete, then the multiplicative integral is an operator product.
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© 2003 Springer-Verlag Berlin Heidelberg
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Gil’, M.I. (2003). 10 Multiplicative Representations of Resolvents. In: Operator Functions and Localization of Spectra. Lecture Notes in Mathematics, vol 1830. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45225-6_10
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DOI: https://doi.org/10.1007/978-3-540-45225-6_10
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20246-2
Online ISBN: 978-3-540-45225-6
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