Examples of infinitely generated function algebras
P. J. de Paepe (2003)
Czechoslovak Mathematical Journal
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Examples of non-finitely generated function algebras on planar sets with small maximal ideal spaces are given.
P. J. de Paepe (2003)
Czechoslovak Mathematical Journal
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Examples of non-finitely generated function algebras on planar sets with small maximal ideal spaces are given.
Jan Čerych (1978)
Commentationes Mathematicae Universitatis Carolinae
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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...
Jana Mervartová (1983)
Archivum Mathematicum
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Antoine, Jean-Pierre, Trapani, Camillo, Tschinke, Francesco (2006)
International Journal of Mathematics and Mathematical Sciences
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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 on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not...
J. Schmidt (1966)
Colloquium Mathematicae
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Jean-Pierre Antoine, Camillo Trapani, Francesco Tschinke (2011)
Studia Mathematica
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We continue our study of topological partial *-algebras, focusing on the interplay between various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between strong and weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *-algebras, emphasizing the crucial role played by appropriate bounded elements, called ℳ-bounded....