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Fernanda Botelho, James Jamison (2010)
Studia Mathematica
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We characterize a class of *-homomorphisms on Lip⁎(X,𝓑(𝓗 )), a non-commutative Banach *-algebra of Lipschitz functions on a compact metric space and with values in 𝓑(𝓗 ). We show that the zero map is the only multiplicative *-preserving linear functional on Lip⁎(X,𝓑(𝓗 )). We also establish the algebraic reflexivity property of a class of *-isomorphisms on Lip⁎(X,𝓑(𝓗 )).
H. Dales (1981)
Studia Mathematica
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Robert Fraser (1969)
Studia Mathematica
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Heiko Berninger, Dirk Werner (2003)
Extracta Mathematicae
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K. de Leeuw (1961)
Studia Mathematica
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J. Grzybowski, D. Pallaschke, R. Urbański (2007)
Control and Cybernetics
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J. A. Johnson (1979)
Colloquium Mathematicae
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Arya Jamshidi, Fereshteh Sady (2013)
Open Mathematics
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In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying...
Robert Fraser (1970)
Fundamenta Mathematicae
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Nguyen Van Khue, Nguyen To Nhu (1981)
Colloquium Mathematicae
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Nik Weaver (1995)
Studia Mathematica
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We abstractly characterize Lipschitz spaces in terms of having a lattice-complete unit ball and a separating family of pure normal states. We then formulate a notion of "measurable metric space" and characterize the corresponding Lipschitz spaces in terms of having a lattice complete unit ball and a separating family of normal states.
J. Wilker (1971)
Fundamenta Mathematicae
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Diethard Pallaschke, Dieter Pumplün (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.