### Relations between exponential laws for spaces of ${C}^{\infty}$-functions.

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This article deals with bounding sets in real Banach spaces E with respect to the functions in A(E), the algebra of real analytic functions on E, as well as to various subalgebras of A(E). These bounding sets are shown to be relatively weakly compact and the question whether they are always relatively compact in the norm topology is reduced to the study of the action on the set of unit vectors in ${l}_{\infty}$ of the corresponding functions in $A\left({l}_{\infty}\right)$. These results are achieved by studying the homomorphisms on the...

By studying algebra homomorphisms, which act as point evaluations on each countable subset, we obtain improved results on the question when all algebra homomorphisms are point evaluations.

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