On some notions of convergence for n-tuples of operators

Daniel Alpay, F. Colombo, I. Sabadini

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7 Scopus citations

Abstract

The aim of this paper is to show that we can extend the notion of convergence in the norm-resolvent sense to the case of several unbounded noncommuting operators (and to quaternionic operators as a particular case) using the notion of S-resolvent operator. With this notion, we can define bounded functions of unbounded operators using the S-functional calculus for n-tuples of noncommuting operators. The same notion can be extended to the case of the F-resolvent operator, which is the basis of the F-functional calculus, a monogenic functional calculus for n-tuples of commuting operators. We also prove some properties of the F-functional calculus, which are of independent interest.

Original languageEnglish
Pages (from-to)2363-2371
Number of pages9
JournalMathematical Methods in the Applied Sciences
Volume37
Issue number16
DOIs
StatePublished - 15 Nov 2014

Keywords

  • Convergence in the norm-resolvent sense
  • F-resolvent operator
  • Properties of the F-functional calculus
  • S-resolvent operator
  • Unbounded and noncommuting operators

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