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Remarks Concerning Uniformly Bounded Operators on Hilbert Space

Published online by Cambridge University Press:  20 November 2018

I. Istrǎțescu
I. Istrǎțescu*
Affiliation:
Politechnic Institute Timişoara, Timişoara, Roumania
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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. 1. sup {‖Tn‖, ‖Sn‖}<∞ (n = 0, ±1, ±2,…)

  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 that

sup ‖Tn‖<∞ (n = 1, 2, 3,…)

is similar to a contraction.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972, pp. 215 - 217
Copyright
Copyright © Canadian Mathematical Society 1972

References

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3. Istrǎțescu, I., On operators with uniformly bounded iterates, Mat. Vestnik, 21 (1969), 373-375.Google Scholar
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