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Generators for algebras dense in L p -spaces

Alexander J. Izzo, Bo Li (2013)

Studia Mathematica

For various L p -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in L p ( μ ) . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...

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