The local reduced minimum modulus on a Hilbert space

Mbekhta, Mostafa

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1007/s44146-023-00060-3

Permalink :

http://hdl.handle.net/20.500.12210/124202

Title :

The local reduced minimum modulus on a Hilbert space

Author(s) :

Mbekhta, Mostafa [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Acta Scientiarum Mathematicarum

Pages :

269-292

Publisher :

Springer / Acta Universitatis Szegediensis

Publication date :

2023-02-27

ISSN :

0001-6969

English keyword(s) :

Reduced minimum modulus, Strength function, Moore–Penrose inverse, Partial isometry.

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Let H be a complex Hilbert space and let B(H) be the algebraof all bounded linear operators on H. In this paper, for T ∈ B(H) and aunit vector x ∈ H, we introduce a local version of the reduced minimummodulus of T at x, ...
Show more >Let H be a complex Hilbert space and let B(H) be the algebraof all bounded linear operators on H. In this paper, for T ∈ B(H) and aunit vector x ∈ H, we introduce a local version of the reduced minimummodulus of T at x, noted by γ(T, x). Properties of this quantity areinvestigated. We study the relations between γ(T, x) and the Moore–Penrose inverse, spectrum of |T| and the local spectrum of |T| at x. Atthe end of this paper we will be interested in several problems aroundthis quantity (preserving, continuity, local spectral theory).Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-02-21T06:53:21Z

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