Monotone operators in Banach spaces

It is the purpose of this dissertation to study monotone operators between Banach spaces. In order to do so it is necessary to introduce the concept of Banach spaces in semiduality. Some of the basic properties of this new definition are established. Monotone, semimonotone and complex-monotone operators between spaces in semiduality are then investigated. Projection techniques are used to establish the major results concerning conditions which imply surjectivity of the different types of monotone mappings. Examples demonstrate that monotone operators from a space to its dual and accretive operators from a space to itself are special cases of monotone mappings between spaces in semiduality. Thus many of the results in these cases are obtained as corollaries.