Regular infinite dimensional Lie groups

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and flat connections integrate to horizontal foliations as in finite dimensions. As consequences we obtain that Lie algebra homomorphisms intergrate to Lie group homomorphisms, if the source group is simply connected and the image group is regular.Comment: AmSTeX, using diag.tex with fonts lams?.ps, 38 page

Differentiable perturbation of unbounded operators

If $A(t)$ is a C^{1,\al}-curve of unbounded self-adjoint operators with compact resolvents and common domain of definition, then the eigenvalues can be parameterized $C^1$ in $t$. If $A$ is $C^\infty$ then the eigenvalues can be parameterized twice differentiable.Comment: amstex 9 pages. Some misprints correcte

A characterization of reduced incidence algebras

AbstractThis paper aims to give a criterium, in terms of the partial ordering on the po-set only, which decides whether or not an equivalence relation on the segments of the po-set is compatible (defined by Doubilet, Rota & Stanley [2] in terms of the convolution and the functions of the incidence algebra)