A complete characterization of bounded and unbounded norm hermitian operators on is given for the case when E is a complex Banach space with trivial multiplier algebra. As a consequence, the bi-circular projections on are determined. We also characterize a subclass of hermitian operators on for a complex Hilbert space.
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.
This paper gives a characterization of surjective isometries on spaces of continuously differentiable functions with values in a finite-dimensional real Hilbert space.
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 )).
This paper characterizes the hermitian operators on spaces of Banach-valued Lipschitz functions.
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