Operator-valued measures and integrals for cone-valued functions / Walter Roth

This is an interesting book which firstly presents an extension of the theory of locally convex topological vector spaces (lctvs) to a more general setting which the same author introduced in the context of approximation problems and named locally convex cones (lcc). New features that appear are due to the possibility of considering elements of infinite type which restrict the cancellation laws and others. Now the context of new material, not well placed in classical lctvs may be treated more easily with the tools of this context. For instance, a main point of the book is to present an extensive theory of integration, which unifies not only the treatment of extended real-valued, vector-valued and operator-valued measures and functions but cone-valued ones as well. The latter is a new topic and forms a principal goal of the oeuvre. ... (Zentralblatt)