Vol. 35, No. 3, 1970

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Cone relationships of biorthogonal systems

S. W. Smith

Vol. 35 (1970), No. 3, 787–794

It is shown in this paper that total biorthogonal systems have the same cone if and only if they differ at most by rearrangement and by positive scalar multiplication. A connection is demonstrated between this result and work done by R. E. Fullerton in which he characterized the existence of an unconditional basis in terms of the existence of certain type cones. The paper is concluded by generalizing the first result to the situation in which two biorthogonal systems have cones which induce order isomorphic orderings.

Mathematical Subject Classification
Primary: 46.06
Received: 26 March 1970
Published: 1 December 1970
S. W. Smith