An Inequality for Bi-orthogonal Pairs  
  Authors: Christopher Meaney,  
  Keywords: Bi-orthogonal pair, Bessel's inequality, Orthogonal expansion, Lebesgue constants.  
  Date Received: 26/11/2009  
  Date Accepted: 14/12/2009  
  Subject Codes:

42C15, 46C05.

  Editors: Sever S. Dragomir,  

We use Salem's method [13, 14] to prove an inequality of Kwapien and Pelczynski concerning a lower bound for partial sums of series of bi-orthogonal vectors in a Hilbert space, or the dual vectors. This is applied to some lower bounds on $L^{1}$ norms for orthogonal expansions.;

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