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The Complex Plank Problem
Author(s) -
Ball Keith M.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1017/s002460930100813x
Subject(s) - plank , mathematics , sequence (biology) , hilbert space , norm (philosophy) , pure mathematics , combinatorics , discrete mathematics , law , genetics , materials science , political science , composite material , biology
It is shown that if( v j ) 1 nis a sequence of norm 1 vectors in a complex Hilbert space and( t j ) 1 nis a sequence of non‐negative numbers satisfying ∑ t j 2 = 1 ,then there is a unit vector z for which| 〈 v j , z 〉 | ⩾ t jfor every j . The result is a strong, complex analogue of the author's real plank theorem.