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Positive Linear Maps of Operator Algebras
This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as...
Classification of Nuclear C*-Algebras. Entropy in Operator Algebras
to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of facto...
Dynamical Entropy in Operator Algebras
The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.
A Taste of Jordan Algebras
This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.
The Joy of Discovery
Walter Thirring is the last offspring of an Austrian family of scientists. In this moving narrative, he describes how he survived the Nazi occupation and became instrumental in reconstructing European science. Thirring is one of the last living physicists who worked on the greatest discoveries and with the greatest scientists of the 20th century. He recollects encounters with the old masters like Einstein, Schrdinger, Heisenberg, Pauli and others as well as his collaborations with the present stars like Murray Gell-Mann and Elliott Lieb. The book presents the challenges faced when one of the major paradigm shifts took place, namely, the shift away from atomistic theory and Newtonian physic...
