Algebraic reflexivity of C(X,E) and Cambern's theorem
The algebraic and topological reflexivity of C(X) and C(X,E) are investigated by using representations for the into isometries due to Holsztyński and Cambern.
Surjective isometries on spaces of differentiable vector-valued functions
This paper gives a characterization of surjective isometries on spaces of continuously differentiable functions with values in a finite-dimensional real Hilbert space.
Homomorphisms on algebras of Lipschitz functions
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 )).
Hermitian operators on Lipschitz function spaces
This paper characterizes the hermitian operators on spaces of Banach-valued Lipschitz functions.
Models of learning and the polar decomposition of bounded linear operators.
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