Schmudgen Konrad An Invitation to Unbounded Representations of Star Algebras on Hilbert Space

This book is devoted to the study of Tomita's observable algebras, their structure and applications.

The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem).

This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion.

The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.

This book introduces readers to the theory of practice architectures and conveys a way of approaching practice theory through developing a practice sensibility. It shows that, in order to change our practices, we must also change the conditions that make those practices possible. The book draws on everyday life to illustrate how we can see the world by watching it unfold in practices: it argues that life happens in practices. The theory of practice architectures takes the ontological nature of practices seriously by recognising that practices take place in the real world.