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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Linear operators for which $T^{\ast } T$ and $TT^{\ast }$ commute
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by Stephen L. Campbell PDF
Proc. Amer. Math. Soc. 34 (1972), 177-180 Request permission

Abstract:

Linear operators T for which ${T^\ast }T$ and $T{T^\ast }$ commute are studied. Examples are given to show that this class of operators is distinct from several other operator classes. It is proven that if ${T^\ast }T$ and $T{T^\ast }$ commute and T is hyponormal, then T has an invariant subspace. A generalization of this theorem is given.
References
  • Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
  • Peter A. Fillmore, Notes on operator theory, Van Nostrand Reinhold Mathematical Studies, No. 30, Van Nostrand Reinhold Co., New York-London-Melbourne, 1970. MR 0257765
  • Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 177-180
  • MSC: Primary 47B99
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0295124-9
  • MathSciNet review: 0295124