Investigation of special Banach spaces of holomorphic, harmonic and real analytic functions

我想邀请卢德科夫斯基教授(莫斯科)到帕德伯恩大学作客三个月。我们想继续研究四元数上的Müntz空间和Banach空间。特别是，我们到目前为止起草的三份文件将完成并提交出版。本文证明了所有关于自反L_p范数的Müntz空间都与L_p同构，而且存在一个关于超范数的Müntz空间，它包含所有其他Müntz空间作为可补子空间。凭借这一特性，这个空间是独一无二的。考虑到这些结果，我们还想要研究是否所有的超范Müntz空间都有Schauder基，并且我们想要处理一个同构的分类。C-Lambda空间可以粗略地视为(单位圆上的)Müntz空间的复类比，类似的问题也应被处理。最后，我们要讨论四元数上Dirac模的Schauder基及相关问题。

I would like to invite Prof. Dr. Ludkovsky (Moskau) als guest for three months at the university of Paderborn. We want to continue our research on Müntz spaces and Banach spaces over quaternions. In particular, our three papers which we drafted so far shall be completed and submitted for publication. We show here that all Müntz spaces with respect to a reflexive L_p norm are isomorphic to l_p. Moreover there is a Müntz space with respect to the sup-norm which contains all other Müntz spaces as complemented subspaces. By this property this space is unique. Taking these results into account we also want to investigate whether all sup-norm Müntz spaces have a Schauder basis and we want to deal with an isomorphic classification. Similar questions shall be treated for C-Lambda spaces which can be roughly regarded as the complex analogues of Müntz spaces (over the unit circle). Finally we want to deal with Schauder bases in Dirac modules over quaternions and related questions.