Vol. 34, No. 2, 1970

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Representation and series summability of complete biorthogonal sequences

William Henry Ruckle

Vol. 34 (1970), No. 2, 511–528
Abstract

Let {xj,xj′} be a complete biorthogonal sequence with each xj in a Banach space X and each xjin 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 xover 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
Milestones
Received: 17 June 1969
Revised: 10 February 1970
Published: 1 August 1970
Authors
William Henry Ruckle