A stronger metric for closed operators in Hilbert space
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- by William E. Kaufman PDF
- Proc. Amer. Math. Soc. 90 (1984), 83-87 Request permission
Abstract:
There is available, for the closed and densely-defined operators in a Hilbert space, a metric which is stronger than the gap metric while sharing many of its properties. On the bounded operators it is equivalent to the metric generated by the usual operator-norm.References
- Tosio Kato, Perturbation theory for linear operators, 2nd ed., Grundlehren der Mathematischen Wissenschaften, Band 132, Springer-Verlag, Berlin-New York, 1976. MR 0407617
- William E. Kaufman, Representing a closed operator as a quotient of continuous operators, Proc. Amer. Math. Soc. 72 (1978), no. 3, 531–534. MR 509249, DOI 10.1090/S0002-9939-1978-0509249-9
- William E. Kaufman, Closed operators and pure contractions in Hilbert space, Proc. Amer. Math. Soc. 87 (1983), no. 1, 83–87. MR 677237, DOI 10.1090/S0002-9939-1983-0677237-X
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 83-87
- MSC: Primary 47A30; Secondary 47D99
- DOI: https://doi.org/10.1090/S0002-9939-1984-0722420-9
- MathSciNet review: 722420