Geodesic
Deficiencies of Certain Real Uniform Algebras
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 121-132

Voir la notice de l'article provenant de la source Cambridge University Press

Let U be a complex uniform algebra, Z and dZ its maximal ideal space and its Šilov boundary, respectively. The Dirichlet (respectively Arens-Singer) deficiency of U is the codimension in CR(∂Z) of the closure of Re U (respectively of the real linear span of log|U -1|). Algebras with finite Dirichlet deficiency have many interesting properties, especially when the Arens-Singer deficiency is zero. (See, e.g. [5].) By a real uniform algebra we mean a real commutative Banach algebra A with identity 1, and norm ‖ ‖ such that ‖f2‖ = ‖f‖ 2 for each fin A 
Limaye, B. V.; Simha, R. R. Deficiencies of Certain Real Uniform Algebras. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 121-132. doi: 10.4153/CJM-1975-015-x
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