Geodesic
Remarks Concerning Uniformly Bounded Operators on Hilbert Space
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 215-217

Voir la notice de l'article provenant de la source Cambridge University Press

In [6] B. Sz.-Nagy has proved that every operator on a Hilbert space such that 1 is similar to a unitary operator.The following problem is an extension of this result: If T and S are two operators such that 1. sup {‖Tn‖, ‖Sn‖}<∞ (n = 0, ±1, ±2,...) 2. TS = ST then there exists a selfadjoint operator Q such that QTQ-1, QSQ-1 are unitary operators?Also, in [7] B. Sz.-Nagy has proved that every compact operator T such thatsup ‖Tn‖<∞ (n = 1, 2, 3,...)is similar to a contraction. 
Istrǎțescu, I. Remarks Concerning Uniformly Bounded Operators on Hilbert Space. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 215-217. doi: 10.4153/CMB-1972-039-7
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