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On ring derivations and quadratic functionals

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In this note the general form of ring derivations on a function algebra is obtained. In particular, we give a very simple proof of the following result of Nandakumar: a ring derivation on a function algebra is trivial provided that the Choquet boundary of the algebra contains a dense sequentially non-isolated set. Using this theorem we prove a result concerning representability of quadratic functionals by bilinear forms.

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This work was supported by the Research Council of Slovenia.

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šemrl, P. On ring derivations and quadratic functionals. Aeq. Math. 42, 80–84 (1991).

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