On normal operator exponentials
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- by Christoph Schmoeger PDF
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Abstract:
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
- Gunter Lumer and Marvin Rosenblum, Linear operator equations, Proc. Amer. Math. Soc. 10 (1959), 32–41. MR 104167, DOI 10.1090/S0002-9939-1959-0104167-0
- Theodore W. Palmer, Banach algebras and the general theory of $^*$-algebras. Vol. I, Encyclopedia of Mathematics and its Applications, vol. 49, Cambridge University Press, Cambridge, 1994. Algebras and Banach algebras. MR 1270014, DOI 10.1017/CBO9781107325777
- C. R. Putnam, Ranges of normal and subnormal operators, Michigan Math. J. 18 (1971), 33–36. MR 276810
- Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815
- Christoph Schmoeger, Über die Eindeutigkeit des Logarithmus eines unitären Operators, Nieuw Arch. Wisk. (4) 15 (1997), no. 1-2, 57–61 (German). MR 1470437
- Christoph Schmoeger, Remarks on commuting exponentials in Banach algebras, Proc. Amer. Math. Soc. 127 (1999), no. 5, 1337–1338. MR 1476391, DOI 10.1090/S0002-9939-99-04701-2
- Ch. Schmoeger: Remarks in commuting exponential in Banach algebras, II. Proc. Amer. Math. Soc. 128 (2000), 3405–3409.
- Edgar M. E. Wermuth, A remark on commuting operator exponentials, Proc. Amer. Math. Soc. 125 (1997), no. 6, 1685–1688. MR 1353407, DOI 10.1090/S0002-9939-97-03643-5
Additional Information
- Christoph Schmoeger
- Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
- Email: christoph.schmoeger@math-uni-karlsruhe.de
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 697-702
- MSC (2000): Primary 47A10, 47A60
- DOI: https://doi.org/10.1090/S0002-9939-01-06123-8
- MathSciNet review: 1866022