Journal article
Do projections stay close together?
- Abstract:
- We estimate the rate of convergence of products of projections on K intersecting lines in Rd. More generally, consider the orbit of a point under any sequence of orthogonal projections on K arbitrary lines in Rd. Assume that the sum of the squares of the distances of the consecutive iterates is less than ε. We show that if ε tends to zero, then the diameter of the orbit tends to zero uniformly for all families L of a fixed number K of lines. We relate this result to questions concerning convergence of products of projections on finite families of closed subspaces of ℓ2. © 2008 Elsevier Inc. All rights reserved.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 253.5KB, Terms of use)
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- Publisher copy:
- 10.1016/j.jmaa.2008.09.039
Authors
- Publisher:
- Elsevier
- Journal:
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS More from this journal
- Volume:
- 350
- Issue:
- 2
- Pages:
- 859-871
- Publication date:
- 2009-02-15
- DOI:
- EISSN:
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1096-0813
- ISSN:
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0022-247X
- Language:
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English
- Keywords:
- Pubs id:
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26491
- UUID:
-
uuid:64281e6f-05d7-46c6-b69b-52a5303ff1c7
- Local pid:
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pubs:26491
- Source identifiers:
-
26491
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier BV
- Copyright date:
- 2009
- Notes:
- Copyright 2008 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/
- Licence:
- Other
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