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THE COMPLEX PLANK PROBLEM

Published online by Cambridge University Press:  25 July 2001

KEITH M. BALL
KEITH M. BALL
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT; kmb@math.ucl.ac.uk
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Abstract

It is shown that if (vj)n1 is a sequence of norm 1 vectors in a complex Hilbert space and (tj)n1 is a sequence of non-negative numbers satisfying

[formula here]

then there is a unit vector z for which

[formula here]

for every j. The result is a strong, complex analogue of the author's real plank theorem.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 4 , July 2001 , pp. 433 - 442
Copyright
© The London Mathematical Society 2001

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