Open AccessOn the hereditary character of certain spectral properties and some applications
Author(s) -
Carlos Carpintero,
Ennis Rosas,
Orlando García,
José Sanabria,
Andrés Malaver
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-3678
Subject(s) - linear subspace , mathematics , invariant subspace , spectral properties , pure mathematics , subspace topology , invariant (physics) , banach space , operator (biology) , character (mathematics) , invariant subspace problem , type (biology) , space (punctuation) , discrete mathematics , mathematical analysis , approximation property , unbounded operator , mathematical physics , physics , computer science , repressor , ecology , chemistry , biology , operating system , biochemistry , geometry , transcription factor , astrophysics , gene
In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that Tn (X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectral properties are transmitted from T to its restriction on W and vice-versa. As consequence of our results, we give conditions for which semiFredholm spectral properties, as well as Weyl type theorems, are equivalent for two given operators. Additionally, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type theorems. In particular, we give some applications of these results for integral operators acting on certain functions spaces.