Invertible composition operators on Hp

Composition Operators and Multiplication Operators on Orlicz Spaces

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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.

On reducibility of weighted composition operators

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

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 ...

A Note on Weighted Composition Operators on L^p-Spaces