Complex symmetry of invertible composition operators

Affine Mappings of Invertible Operators

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

The invertible double of elliptic operators

We construct a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary and derive a natural formula for the Calderón projector which yields a generalization of the famous Cobordism Theorem. Assuming symmetric principal symbol of the tangential operator and unique continuation property (UCP) from the boundary, we obtain the ...

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

Weighted composition operators between Lipschitz algebras of complex-valued bounded functions

‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.

Composition Operators and Several Complex Variables