Ball, K.M.;
(2001)
The complex plank problem.
Bulletin of the London Mathematical Society
, 33
(4)
pp. 433-442.
10.1112/S002460930100813X.
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Abstract
It is shown that if $(v_{j})$ is a sequence of norm $1$ in a complex Hilbert space and $(t_{j})$ is a sequence of nonnegative numbers satisfying $\sum t_{j}^{2}=1$ then there is a unit vector z for which $|\langle v_{j}, z \rangle|\geq t_{j} for every j. The result is a strong, complex analogue of the author's real plank theorem.
| Type: | Article |
|---|---|
| Title: | The complex plank problem |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/S002460930100813X |
| Publisher version: | http://dx.doi.org/10.1112/S002460930100813X |
| Language: | English |
| Additional information: | This is an electronic version of an article published in 'Ball, K.M. (2001) The complex plank problem. Bulletin of the London Mathematical Society, 33 (4). pp. 433-442. ISSN 00246093'. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/12546 |
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