عنوان

State spaces of operator algebras :basic theory, orientations and C*-products

State spaces of operator algebras :basic theory, orientations and C*-products

Boston

Birkhauser

c2001

xii, 350 p. ; 24 cm.

Mathematics : theory & applications

Includes bibliographical references )p. ]341[-344( and index

Erik M. Alfsen, Frederic W. Shultz

Machine generated contents note: Chapter 1: Introduction 1 -- Basic notions from convexity and ordered vector spaces 1 -- Order unit and base norm spaces 9 -- Selected topics in functional analysis 71 -- Spectral theory for monotone complete CR)X(62 -- Elementary dimension theory in lattices 03 -- Ordered algebras 33 -- Algebras with involution 24 -- O rder derivations 55 -- Notes 26 -- Chapter 2: Elementary Theory of C*-algebras and -- von Neumann Algebras36 -- Basics on C*-algebras 36 -- Representations of C*-algebras 87 -- Preliminaries on B)H( 58 -- Basics on von Neumann algebras 101 -- M iscellaneous 121 -- N otes921 -- Chapter 3: Ideals, Faces and Compressions 031 -- Projections, ideals, and faces for von Neumann algebras031 -- Projections, ideals and faces for C*-algebras151 -- Invariant subspaces 161 -- Compressions of von Neumann algebras 861 -- N otes471 -- Chapter 4: The Normal State Space of B)H(671 -- Facial Structure 671 -- The concepts of angle and geodesic metric381 -- *-isomorphisms and *-anti-isomorphisms 981 -- Orientation of balls and multiplication in M2)C(391 -- Notes891 -- Chapter 5: States, Representations, and Orientations of -- C *-algebras991 -- State space geometry and representations 002 -- The spectrum and primitive ideal space 802 -- Completely positive maps 312 -- Orientations of state spaces 512 -- Orientations and C* structures 322 -- Orientations and non-unital C*-algebras 932 -- Notes 042 -- Chapter 6: Symmetries and Rotations in -- von Neumann Algebras142 -- Elements of structure theory142 -- Symmetries and reflections 942 -- Rotational Derivations 562 -- Notes972 -- Chapter 7: Orientations and von Neumann Algebras182 -- Balanced symmetries and associative products282 -- Cartesian triples and 3-frames 592 -- Orientation of normal state spaces413 -- From orientations to associative products 923 -- Notes 043 -- Bibliography 143 -- Index 543

، Operator algebras

، State-space methods

0391-

Alfsen, Erik M. )Erik Magnus(

AU

AU Shultz, Frederic W 1945-

TI

SE

SE Mathematics )Boston, Mass.(