Opuscula Mathematica
Opuscula Math. 46, no. 5 (2026), 751-771

Quasicontractive n-step liftings for operators similar to contractions

Andra-Maria Stoica
Laurian Suciu
Abstract. The paper is devoted to operators \(T\) acting on a Hilbert space \(\mathcal{H}\), that are similar to contractions. In this setting, we investigate quasi-isometric liftings induced by certain intermediate quasicontractive liftings \(Q\) for \(T\), which satisfy the condition \(Q^*Q \mathcal{H}=\mathcal{H}\). Such operators \(Q\) are generated by \(T\) and an operator \(A\), which gives the similarity of \(T\) to a contraction, this meaning that \(A\) is invertible and \(A \geq T^*AT \geq T^*T\). In this setting, we introduce the \(n\)-step liftings of \(T\) with respect to \(A\), which lead to a natural quasi-isometric lifting for \(T\). The aim of this paper is to show that the step-by-step construction of the minimal isometric lifting of a contraction can be adapted to this framework, in order to obtain a minimal quasi-isometric lifting of \(T\).
Keywords: quasicontraction, quasi-isometry, lifting.
Mathematics Subject Classification: 47A05, 47A15, 47A20, 47A63.
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About the authors ▼
Andra-Maria Stoica
https://orcid.org/0009-0000-9989-2253
Lucian Blaga University of Sibiu, Department of Mathematics and Informatics, Romania
Laurian Suciu (corresponding author)
https://orcid.org/0000-0002-5675-0519
Lucian Blaga University of Sibiu, Department of Mathematics and Informatics, Romania
About the article ▼
Communicated by Sergiusz Kużel.
Received: 2026-07-17.
Revised: 2026-09-27.
Accepted: 2026-10-05.
Published online: 2026-10-28.
Cite this article as ▼
Andra-Maria Stoica, Laurian Suciu, Quasicontractive n-step liftings for operators similar to contractions, Opuscula Math. 46, no. 5 (2026), 751-771, https://doi.org/10.7494/OpMath.202610051.
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