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- W2038462076 abstract "The polydisk algebra, A, generated by the n-coordinate functions, ZI ,***, n,, on D” (D denotes the unit disk) identifies with a closed subalgebra of C(7’“) (T denotes the unit circle) and it is natural to study those closed subalgebras of C(P) containing A. Unlike the case for n = 1 (here, A is maximal in C(T) by Wermers maximality theorem), there are many algebras lying properly in between A and C(7”) for n > 1. Although a reasonable characterization of these algebras appears to be exceedingly difficult, the characterization of those whose maximal ideal spaces imbed “nicely” inside D” ‘is accomplished by Theorems I and I’. Theorem I also generalizes Hartog’s classical extension theorem [3; Theorem 5, Chap. I, Sect. C, p. 201, giving rise to a large class of “extension” subsets of D”, of which its topological boundary is but one example. Other examples relating to a certain class of subalgebras of C(P) containing A occur in Section iii." @default.
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- W2038462076 date "1981-08-01" @default.
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- W2038462076 title "A generalization of Hartog's theorem relating to the subalgebras of continuous functions on the n-dimensional torus" @default.
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- W2038462076 doi "https://doi.org/10.1016/0022-1236(81)90036-7" @default.
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