Local definitizability of \(T^{[\ast]}T\) and \(TT^{[\ast]}\)

DOI10.1007/S00020-011-1913-0zbMath1272.47006arXiv1004.1584OpenAlexW1638500461MaRDI QIDQ429731

Friedrich Philipp, Michał Wojtylak, André C. M. Ran

Publication date: 20 June 2012

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.1584

zbMATH Keywords

spectrumKrein spacecritical pointdefinitizable operator

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Linear operators on spaces with an indefinite metric (47B50)

Related Items (4)

Certain properties involving the unbounded operators \(p(T)\), \(TT^\ast\), and \(T^\ast T\); and some applications to powers and \textit{nth} roots of unbounded operators ⋮ Right (or left) invertibility of bounded and unbounded operators and applications to the spectrum of products ⋮ Spectral functions of products of selfadjoint operators ⋮ \(\mathcal{J}\)-selfadjoint Krein space operators and Aluthge transforms

Cites Work

• The pair of operators \(T^{[*}T\) and \(TT^{[*]}\): \(J\)-dilations and canonical forms]
• Corrigendum to: A Krein space approach to \(PT\) symmetry
• A Krein space approach to \(PT\) symmetry
• Analysis of spectral points of the operators \(T^{[*} T\) and \(TT ^{[*]}\) in a Krein space]
• On a class of selfadjoint operators in Krein space and their compact perturbations
• Locally definite operators in indefinite inner product spaces
• Spectral points of type \(\pi_{+}\) and \(\pi_{-}\) of self-adjoint operators in Krein spaces
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