We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and smooth G-manifolds M modelled locally convex spaces. As a tool, we discuss existence uniqueness questions for differential equations given by time-dependent fundamental vector fields are L1 in time. then the closures reachable sets controls algebra g G, or within compact subset g. Regularity pr...

In this article, we shall discuss some recent developments and applications of the local spectral theory for linear operators on Banach spaces. Special emphasis will be given to those parts of operator theory, where spectral theory, harmonic analysis, and the theory of Banach algebras overlap and interact. Along this line, we shall present the recent progress of the theory of quotients and rest...