Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On normal operator exponentials

Author: Christoph Schmoeger
Journal: Proc. Amer. Math. Soc. 130 (2002), 697-702
MSC (2000): Primary 47A10, 47A60
Published electronically: June 20, 2001
MathSciNet review: 1866022
Full-text PDF

Abstract | References | Similar Articles | Additional Information


Suppose that $A$ and $B$ are bounded normal operators on a complex Hilbert space and that $e^A e^B = e^B e^A$. In this paper some conditions implying $AB = BA$ are given.

References [Enhancements On Off] (What's this?)

  • 1. G. Lumer and M. Rosenblum: Linear operator equations. Proc. Amer. Math. Soc. 10 (1959), 32-41. MR 21:2927
  • 2. T. W. Palmer: Banach algebras and the general theory of$ ^{\ast}$-algebras. Vol. I, Cambridge University Press, 1994. MR 95c:46002
  • 3. C. R. Putnam: Ranges of normal and subnormal operators. Michigan Math. J. 18 (1971), 33-36. MR 43:2550
  • 4. W. Rudin: Functional Analysis. Second edition, McGraw-Hill (1991). MR 92k:46001
  • 5. Ch. Schmoeger: Über die Eindeutigkeit des Logarithmus eines unitären Operators. Nieuw Arch. Wisk., 15, no. 1-2 (1997), 57-61. MR 98j:47036
  • 6. Ch. Schmoeger: Remarks on commuting exponentials in Banach algebras. Proc Amer. Math. Soc. 127 (1999), 1337-1338. MR 99h:46090
  • 7. Ch. Schmoeger: Remarks in commuting exponential in Banach algebras, II. Proc. Amer. Math. Soc. 128 (2000), 3405-3409. CMP 2000:17
  • 8. E. M. E. Wermuth: A remark on commuting operator exponentials. Proc. Amer. Math. Soc. 125 (1997), 1685-1688. MR 97g:39011

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A10, 47A60

Retrieve articles in all journals with MSC (2000): 47A10, 47A60

Additional Information

Christoph Schmoeger
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Keywords: Normal operators, exponentials
Received by editor(s): April 3, 2000
Received by editor(s) in revised form: August 20, 2000
Published electronically: June 20, 2001
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society