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THE LINEAR SPAN OF PEAK FUNCTIONS
Alexander J. Izzo
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 3 / October 2005

Published online by Cambridge University Press:

15 September 2005, pp. 631-634
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It is shown that given a uniform algebra $A$ and a peak point $x_0$ for $A$, every function in $A$ can be expressed as a linear combination of two functions in $A$ that peak at $x_0$.

Interpolation problem for l1 and a uniform algebra
Part of
- Commutative Banach algebras and commutative topological algebras
Takahiko Nakazi
Journal:

Journal of the Australian Mathematical Society / Volume 72 / Issue 1 / February 2002

Published online by Cambridge University Press:

09 April 2009, pp. 1-12

Print publication:

February 2002
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Let A be a uniform algebra and M(A) the maximal ideal space of A. A sequence {an} in M(A) is called l1-interpolating if for every sequence (αn) in l1 there exists a function f in A such that f (an) = αn for all n. In this paper, an l1-interpolating sequence is studied for an arbitrary uniform algebra. For some special uniform algebras, an l1-interpolating sequence is equivalent to a familiar l-interpolating sequence. However, in general these two interpolating sequences may be different from each other.

M-Ideals and Function Algebras
K. Seddighi, H. Zahedani
Journal:

Canadian Mathematical Bulletin / Volume 36 / Issue 1 / 01 March 1993

Published online by Cambridge University Press:

20 November 2018, pp. 123-128

Print publication:

01 March 1993
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Let C(X) be the space of all continuous complex-valued functions defined on the compact Hausdorff space X. We characterize the M-ideals in a uniform algebra A of C(X) in terms of singular measures. For a Banach function algebra B of C(X) we determine the connection between strong hulls for B and its peak sets. We also show that M(X) the space of complex regular Borel measures on X has no M-ideal.