Mathematical Quantization by Nik Weaver

Mathematical Quantization by Nik Weaver

With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics. Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras. In the first half of the book, the author quickly builds the operator algebra setting. He uses this as a unifying theme in the second half, in which he treats several active research topics, some for the first time in book form. These include the quantum plane and tori, operator spaces, Hilbert modules, Lipschitz algebras, and quantum groups. For graduate students, Mathematical Quantization offers an ideal introduction to a research area of great current interest. For professionals in operator algebras and functional analysis, it provides a readable tour of the current state of the field.

SKU	Unavailable
ISBN 13	9781584880011
ISBN 10	1584880015
Title	Mathematical Quantization
Author	Nik Weaver
Series	Studies In Advanced Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	Taylor & Francis Inc
Year published	2001-05-31
Number of pages	296
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.