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Hilbert space idempotents and involutions


Author: Don Buckholtz
Journal: Proc. Amer. Math. Soc. 128 (2000), 1415-1418
MSC (1991): Primary 46C05; Secondary 47A05, 47A30
DOI: https://doi.org/10.1090/S0002-9939-99-05233-8
Published electronically: October 5, 1999
MathSciNet review: 1653425
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Abstract | References | Similar Articles | Additional Information

Abstract: Norms of idempotents, involutions, and the Hermitian and skew-Hermitian parts of involutions are shown to be elementary trigonometric functions of an angle between two subspaces of Hilbert space. When the spaces involved are nontrivial, the norm of a linear idempotent is the cosecant of the angle between its range and kernel; the norm of a linear involution is the cotangent of half the angle between the involution's eigenspaces.


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

  • 1. Don Buckholtz, Inverting the difference of Hilbert space projections, Amer. Math. Monthly 104 (1997), 60-61. MR 98a:47002
  • 2. Frank Deutsch, von Neumann's alternating method: the rate of convergence, ``Approximation Theory IV'', C. Chui, L. Schumaker, J. Ward, eds., Academic Press, New York, London, 1983, 427-434. MR 85m:41040
  • 3. Paul R. Halmos, A Hilbert space problem book, 2nd edition, Springer-Verlag, New York, 1982. MR 84e:47001

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Additional Information

Don Buckholtz
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: mat236@ukcc.uky.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05233-8
Received by editor(s): October 25, 1996
Received by editor(s) in revised form: July 2, 1998
Published electronically: October 5, 1999
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 2000 American Mathematical Society

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