Displaying similar documents to “Blaschke inductive limits of uniform algebras.”

Real linear isometries between function algebras. II

Osamu Hatori, Takeshi Miura (2013)

Open Mathematics

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We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

Multiplicatively and non-symmetric multiplicatively norm-preserving maps

Maliheh Hosseini, Fereshteh Sady (2010)

Open Mathematics

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Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖X and ‖.‖Y denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖Y = ‖fg‖X, for certain elements f and g in the domain. Then we show that if α ∈ ℂ 0 and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖X = ‖Tf...

Real-linear isometries between function algebras

Takeshi Miura (2011)

Open Mathematics

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Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → z ∈ ℂ: |z| = 1, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and T f = κ f o φ ¯ on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not...

On peaks in carrying simplices

Janusz Mierczyński (1999)

Colloquium Mathematicae

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A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka-Volterra type that result translates into a simple condition on the coefficients.