Extending positive definite linear forms
Jesús Gil de Lamadrid
Proc. Amer. Math. Soc. 91 (1984), 593-594
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Abstract: In the classical literature two properties, called here symmetry and bounded variation, of a positive definite linear form on an involutive Banach algebra are given. Together they form a necessary and sufficient condition that admit a positive definite linear extension to the involutive algebra obtained from by adjoining an identity. In this note we show that bounded variation alone suffices, in that it already implies symmetry.
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Involutive Banach algebras,
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