Year: 2025
Type: article
Abstract: The aim of this work is to study new properties of the Drazin-Star and the Star-Drazin inverses of a bounded finite potent operator on a Hilbert space. Given a bounded finite potent operator $$\varphi \in \operatorname {End}_k (\mathcal H)$$ φ ∈ End k ( H ) , we prove that the pseudo-characteristic polynomials of $$\varphi ^{D,*}$$ φ D , ∗ and $$\varphi ^{*,D}$$ φ ∗ , D coincide. Accordingly, we obtain that $$\sigma (\varphi ^{D,*}) = \sigma (\varphi ^{*,D})$$ σ ( φ D , ∗ ) = σ ( φ ∗ , D ) , $$\operatorname {Tr}_\mathcal {H} (\varphi ^{D,*}) = \operatorname {Tr}_\mathcal {H} (\varphi ^{*,D})$$ Tr H ( φ D , ∗ ) = Tr H ( φ ∗ , D ) and $$\operatorname {det}_\mathcal {H} (\text {Id} + \varphi ^{D,*}) = \operatorname {det}_\mathcal {H} (\text {Id} + \varphi ^{*,D})$$ det H ( Id + φ D , ∗ ) = det H ( Id + φ ∗ , D ) . In particular, these results hold for a finite square complex matrix A . Moreover, we offer the explicit characterization of the AST-decompositions of
Authors: Fernando Pablos Romo, Dijana Mosić
Institutions: Universidad de Salamanca, University of Nis
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,490
Award: G584303426
OpenAlex ID: W4416951726