Camillo Trapani - Böcker

This book offers a review of the theory of locally convex quasi *-algebras, authored by two of its contributors over the last 25 years. Quasi *-algebras are partial algebraic structures that are motivated by certain applications in Mathematical Physics. They arise in a natural way by completing a *-algebra under a locally convex *-algebra topology, with respect to which the multiplication is separately continuous. Among other things, the book presents an unbounded representation theory of quasi *-algebras, together with an analysis of normed quasi *-algebras, their spectral theory and a study of the structure of locally convex quasi *-algebras. Special attention is given to the case where the locally convex quasi *-algebra is obtained by completing a C*-algebra under a locally convex *-algebra topology, coarser than the C*-topology.Introducing the subject to graduate students and researchers wishing to build on their knowledge of the usualtheory of Banach and/or locally convex algebras, this approach is supported by basic results and a wide variety of examples.

This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.

This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015.