Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-99-05233-8
Published electronically: October 5, 1999
MathSciNet review: 1653425
Full-text PDF Free Access

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), no. 1, 60–61. MR 1426419, https://doi.org/10.2307/2974825
  • 2. Frank Deutsch, von Neumann’s alternating method: the rate of convergence, Approximation theory, IV (College Station, Tex., 1983) Academic Press, New York, 1983, pp. 427–434. MR 754371
  • 3. Paul Richard Halmos, A Hilbert space problem book, 2nd ed., Graduate Texts in Mathematics, vol. 19, Springer-Verlag, New York-Berlin, 1982. Encyclopedia of Mathematics and its Applications, 17. MR 675952

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46C05, 47A05, 47A30

Retrieve articles in all journals with MSC (1991): 46C05, 47A05, 47A30


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