Products of orthogonal projections

Oikhberg, Timur

doi:10.1090/S0002-9939-99-05255-7

Products of orthogonal projections
HTML articles powered by AMS MathViewer

by Timur Oikhberg PDF

Proc. Amer. Math. Soc. 127 (1999), 3659-3669 Request permission

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

Dan Amir, Characterizations of inner product spaces, Operator Theory: Advances and Applications, vol. 20, Birkhäuser Verlag, Basel, 1986. MR 897527, DOI 10.1007/978-3-0348-5487-0
John B. Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR 1070713
R. J. H. Dawlings, The idempotent generated subsemigroup of the semigroup of continuous endomorphisms of a separable Hilbert space, Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), no. 3-4, 351–360. MR 709728, DOI 10.1017/S0308210500015717
J. A. Erdos, On products of idempotent matrices, Glasgow Math. J. 8 (1967), 118–122. MR 220751, DOI 10.1017/S0017089500000173
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056
Kung Hwang Kuo and Pei Yuan Wu, Factorization of matrices into partial isometries, Proc. Amer. Math. Soc. 105 (1989), no. 2, 263–272. MR 977922, DOI 10.1090/S0002-9939-1989-0977922-1
Kung Hwang Kuo and Pei Yuan Wu, Products of orthogonal projections, Functional analysis & related topics (Sapporo, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 127–137. MR 1148612
Pier Luigi Papini, Some questions related to the concept of orthogonality in Banach spaces. Orthogonal projections, Boll. Un. Mat. Ital. (4) 9 (1974), 386–401 (English, with Italian summary). MR 0355540