|
Products of orthogonal projections
Author(s):
Timur
Oikhberg
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3659-3669.
MSC (1991):
Primary 47A68;
Secondary 47D03
Posted:
May 17, 1999
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give a characterization of operators on a separable Hilbert space of norm less than one that can be represented as products of orthogonal projections and give an estimate on the number of factors. We also describe the norm closure of the set of all products of orthogonal projections.
References:
- [A]
- D. Amir, Characterizations of inner product spaces, Birkhäuser-Verlag, Basel, 1986. MR 88m:46001
- [C]
- J. B. Conway, A course in functional analysis, Springer-Verlag, New York, 1990.MR 91e:46001
- [D]
- R. J. H. Dawlings, The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space, Proc. Roy. Soc. Edinburgh 94A (1983), 351-360. MR 85d:47044
- [E]
- J. A. Erdos, On products of idempotent matrices, Glasgow Math. J. 8 (1967), 118-122. MR 36:3803
- [LT]
- J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Springer-Verlag, Heidelberg, 1977. MR 58:17766
- [KW1]
- K.-H. Kuo and P. Y. Wu, Factorization of matrices into partial isometries, Proc. Amer. Math. Soc. 105 (1989), 263-272.MR 89m:15008
- [KW2]
- K.-H. Kuo and P. Y. Wu, Products of orthogonal projections, Functional analysis and related topics (Proceedings of international symposium in Sapporo), World Scientific, Singapore, 1991, pp. 127-137. MR 93b:47003
- [P]
- P. L. Papini, Some questions related to the concept of orthogonality in Banach spaces. Orthogonal projections, Bull. Unione Mat. Ital. (4) 9 (1974), 386-401. MR 50:8014
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
47A68,
47D03
Retrieve articles in all Journals with MSC
(1991):
47A68,
47D03
Additional Information:
Timur
Oikhberg
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
Email:
timur@math.utexas.edu
DOI:
10.1090/S0002-9939-99-05255-7
PII:
S 0002-9939(99)05255-7
Keywords:
Hilbert space,
orthogonal projections
Received by editor(s):
February 20, 1998
Posted:
May 17, 1999
Additional Notes:
This research was supported in part by the National Science Foundation through the Workshop in Linear Analysis at Texas A&M University and by Texas Advanced Research Program Grant 160766.
Communicated by:
David R. Larson
Copyright of article:
Copyright
1999,
American Mathematical Society
|
Comments: webmaster@ams.org