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Deficiencies of Certain Real Uniform Algebras

Published online by Cambridge University Press:  20 November 2018

B. V. Limaye  and
R. R. Simha
B. V. Limaye
Affiliation:
Tata Institute of Fundamental Research, Bombay, India
R. R. Simha
Affiliation:
Tata Institute of Fundamental Research, Bombay, India
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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

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 121 - 132
Copyright
Copyright © Canadian Mathematical Society 1975

References

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