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polynomials and analytic functions on banach spaces

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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The algebra of symmetric analytic functions on L∞
Part of
Pablo Galindo, Taras Vasylyshyn, Andriy Zagorodnyuk
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 4 / August 2017

Published online by Cambridge University Press:

31 May 2017, pp. 743-761

Print publication:

August 2017
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We consider the algebra of holomorphic functions on L∞ that are symmetric, i.e. that are invariant under composition of the variable with any measure-preserving bijection of [0, 1]. Its spectrum is identified with the collection of scalar sequences such that is bounded and turns to be separable. All this follows from our main result that the subalgebra of symmetric polynomials on L∞ has a natural algebraic basis.