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Representation and
series summability of complete biorthogonal sequences
William Henry Ruckle |
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Vol. 34 (1970), No. 2, 511–528
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Abstract |
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Let {xj,xj′} be a complete biorthogonal sequence with each xj in a Banach space X and each xj′ in the conjugate space x∗. A study is made of the summability properties of the series Σjxj′(x)xj and ΣJxj′(x)x′(xj) as x ranges over X and x′ over x∗. Conditions are given for matrix and abstract methods of series summability for these series in terms of certain sequence spaces which arise naturally in connection with the biorthogonal sequence. |
Mathematical Subject Classification
Primary: 40.50
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Milestones
Received: 17 June 1969
Revised: 10 February 1970
Published: 1 August 1970
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Authors |
| William Henry Ruckle | |
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