### Abstract

A notion of regularity and singularity for a special class of operators acting in a rigged Hilbert space D⊂H⊂D× is proposed and it is shown that each operator decomposes into a sum of a regular and a singular part. This property is strictly related to the corresponding notion for sesquilinear forms. A particular attention is devoted to those operators that are neither regular nor singular, pointing out that a part of them can be seen as perturbation of a self-adjoint operator on H. Some properties for such operators are derived and some examples are discussed.

Lingua originale | English |
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pagine (da-a) | 2011-2024 |

Numero di pagine | 14 |

Rivista | Mediterranean Journal of Mathematics |

Volume | 13 |

Stato di pubblicazione | Published - 2016 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)