## 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 language | English |
---|---|

Pages (from-to) | 2363-2371 |

Number of pages | 9 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 37 |

Issue number | 16 |

DOIs | |

State | Published - 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