Abstract
Let T be an operator on a separable Hubert space. We show that if T is a compact operator and satisfies ∣Tn∣ = ∣T∣n for some n, then T is normal, and that if T is a bounded operator and satisfies ∣Tn∣ = ∣T∣n for n =i,i + 1, k,k + 1 (1 ≤ i <k), then the polar decomposition of T is commutative. For a closed operator we obtain the analogous results.
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Dedicated to Professor Tsuyoshi Ando on his sixtieth birthday
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© 1993 Springer Basel AG
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Uchiyama, M. (1993). Operators which have Commutative Polar Decompositions. In: Furuta, T., Gohberg, I., Nakazi, T. (eds) Contributions to Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 62. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8581-2_12
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DOI: https://doi.org/10.1007/978-3-0348-8581-2_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9690-0
Online ISBN: 978-3-0348-8581-2
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