02226nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001700171084001500188100002600203245009300229260008200322300003400404336002600438337002600464338003600490347002400526490006100550506006600611520105100677650003201728650002901760856003501789856006401824262-210305CH-001817-320210305234504.0a fot ||| 0|cr nn mmmmamaa210305e20210401sz fot ||| 0|eng d a978398547504970a10.4171/ELM/322doi ach0018173 7aPBKG2bicssc a46-xx2msc1 aHiai, Fumio,eauthor.10aLectures on Selected Topics in von Neumann Algebrash[electronic resource] /cFumio Hiai3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (250 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe theory of von Neumann algebras, originating with the work of F. J. Murray and J. von Neumann in the late 1930s, has grown into a rich discipline with connections to different branches of mathematics and physics. Following the breakthrough of Tomita–Takesaki theory, many great advances were made throughout the 1970s by H. Araki,
A. Connes, U. Haagerup, M. Takesaki and others.
These lecture notes aim to present a fast-track study of some important topics in classical parts of von Neumann algebra theory that were developed in the 1970s. Starting with Tomita–Takesaki theory, this book covers topics such as the standard form, Connes’ cocycle derivatives, operator-valued weights, type III structure theory and non-commutative integration theory.
The self-contained presentation of the material makes this book useful not only to graduate students and researchers who want to know the fundamentals of von Neumann algebras, but also to interested undergraduates who have a basic knowledge of functional analysis and measure theory.07aFunctional analysis2bicssc07aFunctional analysis2msc40uhttps://doi.org/10.4171/ELM/32423cover imageuhttps://www.ems-ph.org/img/books/hiai_mini.jpg