Vol. 29, No. 2, 1969

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Multiplier algebras of biorthogonal systems

Raymond J. McGivney and William Henry Ruckle

Vol. 29 (1969), No. 2, 375–387

Let {ei,Ei} be a total biorthogonal system in a linear topological space X. The multiplier algebra of X with respect to {ei,Ei} written M(X) is the set of all scalar sequences (t(i)) such that for each x X there is y X with

Ei(y) = t(i)Ei(x).

The form of M(X) is determined when {ei,Ei} is a norming complete biorthogonal system in a Banach space or a basis in a complete barreled space. It is shown that a sequence space is the multiplier algebra for a basis in a Banach space if and only if it is a γ-perfect BK-algebra.

Mathematical Subject Classification 2000
Primary: 46A45
Received: 5 August 1968
Published: 1 May 1969
Raymond J. McGivney
William Henry Ruckle