Abstract
Weights correspond precisely to measures on a space equipped with a σ-algebra. Not all von Neumann algebras admit a faithful normal state. In fact, even in the separable case, to restrict ourselves to bounded functionals prevents us from developing the theory naturally, which will become clearer in the later chapters such as in Chapter XII.
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Notes on Chapter VII
F. Combes, Poids associés a une algèbre hilbertienne à gauche, Compos. Math., 23 (1971), 49–77.
M. Enock and J M. Schwartz, Kac alagebras and duality of locally compact groups,Springer-Verlag (1992), x + 257.
D. E. Evans and Y. Kawahigashi, Quantum symmetries on operator algebras,Oxford Mathematical Monographs. Oxford Science Publications. Oxford University Press, New York (1998), xvi + 829.
P. Eymard, L’algèbre de Fourier d’un groupe localement compact,Bull. Math. Soc. France, 92 (1964) 181–236.
T. Fack and H. Kosaki, Generalized s-numbers of r -measurable operators, Pacific J. Math., 123 (1986), 269–300.
S. M. Srivastava, A course on Borel sets, Graduate Texts in Math,Springer-Verlag, 180 (1998), xvi + 261.
W. Stinespring, Integration theorems for gages and duality for unimodular groups, Trans. Amer. Math. Soc., 90 (1959), 15–56.
E. Stormer, On infinite tensor products of von Neumann algebras, Amer. J. Math., 93 (1971), 810–818.
E. Sttrmer, Hyperfinite product factors, Ark. Mat., 9 (1971), 165–170. II, J. Funct. Anal., 10 (1972), 471–481. III, Amer. J. Math., 97 (1975), 589–595.
E. St0rmer, Spectra of states, and asymptotically abelian C* -algebras, Comm. Math. Phys., 28 (1972), 279–294. Corrections, ibid., 38 (1974), 341–343.
C. E. Sutherland, Direct integral theory for weights and the Plancherel formula, Bull. Amer. Math. Soc., 20 (1974), 456–461.
C. E. Sutherland, Notes on orbit equivalence: Krieger’s Theorem,Lecture Notes Series, No. 23 (1976), Oslo.
C. E. Sutherland, A Borel parametrization of Polish groups, Publ. Res. Inst. Math. Sci., 21 (1985), 1067–1086.
C. E. Sutherland and M. Takesaki, Actions of discrete amenable groups and groupoids on von Neumann algebras, Publ. Res. Inst. Math. Sci., 21 (1985), 1087–1120.
C. E. Sutherland and M. Takesaki, Actions of discrete amenable groups on injective factors of type III,,l 1, Pacific J. Math., 137 (1989), 405–144.
N. Suzuki, A Linear representation of a countably infinite group, Proc. Japan Acad., 34 (1958), 575–579.
N. Suzuki, Crossed products of rings of operators, Tôhoku Math. J., 11 (1959), 113–124.
H. Takai, On a duality for crossed products of C* -algebras, J. Funct. Anal., 19 (1975), 25–39.
Z. Takeda, Inductive limit and infinite direct product of operator algebras, Tôhoku Math. J., 7 (1955), 67–86.
O. Takenouchi, On type classification of factors constructed as infinite tensor products, Publ. Res. Inst. Math. Sci., 4 (1968), 467–482.
M. Takesaki, Covariant representations of C* -algebras and their automorphism groups, Acta Math., 119 (1967), 273–302.
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Takesaki, M. (2003). Weights. In: Theory of Operator Algebras II. Encyclopaedia of Mathematical Sciences, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10451-4_2
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