TY  - JOUR
ID  - Stoica2026
LB  - Stoica2026
AU  - Stoica, Andra-Maria
AU  - Suciu, Laurian
TI  - Quasicontractive n-step liftings for operators similar to contractions
ST  - Quasicontractive n-step liftings for operators similar to contractions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 5
SP  - 751
EP  - 771
DO  - https://doi.org/10.7494/OpMath.202610051
UR  - https://doi.org/10.7494/OpMath.202610051
AB  - 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 \(T\).
KW  - quasicontraction
KW  - quasi-isometry
KW  - lifting
SN  - 1232-9274
ER  -