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Volume 10, Issue 4, Article 94 |
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An Inequality for Bi-orthogonal Pairs
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Authors: |
Christopher Meaney, |
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Keywords:
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Bi-orthogonal pair, Bessel's inequality, Orthogonal expansion, Lebesgue constants. |
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Date Received:
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26/11/2009 |
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Date Accepted:
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14/12/2009 |
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Subject Codes: |
42C15, 46C05.
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Editors: |
Sever S. Dragomir, |
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Abstract: |
We use Salem's method [13, 14] to prove an inequality of Kwapien and Pe czynski 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  norms for orthogonal expansions.
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