On quantales that classify -algebras
David Kruml, Pedro Resende (2004)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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David Kruml, Pedro Resende (2004)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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S. Sakai (1971)
Bulletin de la Société Mathématique de France
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Şerban Strǎtilǎ, Dan Voiculescu (1982)
Banach Center Publications
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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.
Volker Runde (1994)
Studia Mathematica
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Let A be an A*-algebra with enveloping C*-algebra C*(A). We show that, under certain conditions, a homomorphism from C*(A) into a Banach algebra is continuous if and only if its restriction to A is continuous. We apply this result to the question in the title.
Andrzej Walendziak (2007)
Mathematica Slovaca
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Daniele Guido, Lars Tuset (2001)
Fundamenta Mathematicae
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Suppose B is a unital algebra which is an algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X (Theorem 2.6). Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described (Theorem...
W. Żelazko (1998)
Studia Mathematica
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We show that an arbitrary irreducible representation T of a real or complex algebra on the F-space (s), or, more generally, on an arbitrary infinite (topological) product of the field of scalars, is totally irreducible, provided its commutant is trivial. This provides an affirmative solution to a problem of Fell and Doran for representations on these spaces.