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Hilbert space idempotents and involutions
Author(s):
Don
Buckholtz
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1415-1418.
MSC (1991):
Primary 46C05;
Secondary 47A05, 47A30
Posted:
October 5, 1999
MathSciNet review:
1653425
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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:
- 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:
10.1090/S0002-9939-99-05233-8
PII:
S 0002-9939(99)05233-8
Received by editor(s):
October 25, 1996
Received by editor(s) in revised form:
July 2, 1998
Posted:
October 5, 1999
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
2000,
American Mathematical Society
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