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In this work we generalize some of the previously known adiabatic theorems tosituations with non-unitary evolutions in Banach spaces. We prove adiabatictheorems with uniform gap condition (generalizing a theorem of Abou Salem),adiabatic theorems with non-uniform gap condition (generalizing a theorem ofKato) and qualitative as well as quantitative adiabatic theorems without gapcondition (generalizing theorems of Avron and Elgart, and Teufel).Additionally, we give a generalized version of an adiabatic theorem of higherorder due to Nenciu. In all these adiabatic theorems the considered spectralvalues need not lie on the imaginary axis and in the adiabatic theorems withspectral gap condition and the adiabatic theorem of higher order compactsubsets of the spectrum are sufficient (in particular, these subsets need notconsist of eigenvalues). We explore the strength of the presented adiabatictheorems in numerous examples. In particular, we show that the theorems of thepresent work are more general than the previously known theorems.  This work was finished in October 2010 and handed in as a diploma thesis atthe mathematics department of the University of Stuttgart. The more recentresults of Avron, Fraas, Graf und Grech which appeared in the meantime (in June2011) are therefore not taken into consideration here. We point out, however,that the theorems of the present work are more general than the correspondingtheorems of Avron, Fraas, Graf und Grech - with the exception of the adiabatictheorem of higher order which is in no logical relation to the adiabatictheorem of higher order of Avron, Fraas, Graf and Grech.  We are about to gather the most important theorems of the present work in anarticle and will upload it to arXiv soon.

Adiabatens\"atze mit und ohne Spektrall\"uckenbedingung