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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hilbert space idempotents and involutions


Author: Don Buckholtz
Journal: Proc. Amer. Math. Soc. 128 (2000), 1415-1418
MSC (1991): Primary 46C05; Secondary 47A05, 47A30
Published electronically: 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.


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Additional Information

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

DOI: http://dx.doi.org/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
Published electronically: October 5, 1999
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 2000 American Mathematical Society