Abstract
Every Glimm ideal of anAW *-algebra is a (minimal) primitive ideal.
Similar content being viewed by others
References
Archbold R. J.,On factorial states of operator algebras, J. Funct. Anal.,55 (1984), 25–38.
Batty C. J. K.,Irreducible representation of inseparable C *-algebras, Rocky Mountain J. Math.,14 (1984), 721–727.
Berberian S. K.,Baer*-rings, Springer, Berlin, 1972.
Dixmier J.,Sur les C *-algébres, Bull. Soc. Math. France,88 (1960), 95–112.
Elliott G. A.,On derivations of AW *-algebras, Tôhoku Math. J.,30 (1978), 263–276.
Elliott G. A., Saitô K., Wright J. D. M.,Embedding AW *-algebras as double commutants in type I algebras, J. London Math. Soc.,28 (1983), 376–384.
Feldman J.,Some connections between topological and algebraic properties in rings of operators, Duke Math. J.,23 (1956), 365–370.
Glimm J.,A Stone-Weierstrass theorem for C *-algebras, Ann. of Math.,72 (1960), 216–244.
Hall A.,Doctoral Dissertation, (Newcastle upon Tyne, 1972).
Halpern H.,The maximal GCR-ideal in an AW *-algebra, Proc. Amer. Math. Soc.,17 (1966), 906–914.
Halpern H.,Irreducible module homomorphisms of von Neumann algebra into its center, Trans. Amer. Math. Soc.,140 (1969), 195–221.
Halpern H.,Primitive ideals in von Neumann algebras, Proc. Amer. Math. Soc.,39 (1973), 563–566.
Halpern H.,The norm of an inner derivation of an AW *-algebra, Unpublished Note.
Kadison R. V., Ringrose J. R.,Fundamentals of the theory of operator algebras vol. I and vol. II, Academic Press, London-Orlando, 1983 and 1986.
Kaplansky I.,The structure of certain operator algebras, Trans. Amer. Math. Soc.,70 (1951), 219–255.
Kaplasky I.,Modules over operator algebras, Amer. J. Math.,75 (1953), 839–853.
Nakai M.,Some expectations in AW *-algebras, Proc. Japan Acad.,34 (1958), 411–416.
Ozawa M., Saitô K.,Embeddable AW *-algebras and regular completions, J. London Math. Soc.,34 (1986), 511–523.
Pedersen G. K.,C *-algebras and their automorphism groups, Academic Press, London-New York-San Francisco, 1979.
Saitô K.,Wild, type III, monotone complete, simple C *-algebras indexed by cardinal numbers, J. London math. Soc.,49 (1994), 543–554.
Saitô K., Wright J. D. M.,Ideals of Factors, Rend. Circ. Mat. di Palermo,55 (2006), 360–368.
Somerset D.,The local multiplier algebras of a C *-algebra II, J. Funct. Anal.,171 (2000), 308–330.
Takesaki M.,On the Hahn-Banach type theorem and the Jordan decomposition of module linear mappings over some operator algebras, Kodai Math. Sem. Rep.,12 (1960), 1–10.
Takesaki M.,Theory of operator algebras I, Springer-New York-Heidelberg-Berlin, 1979.
Vincent-Smith G.,The Hahn-Banach theorem for modules, Proc. London Math. Soc.,17 (1967), 72–90.
Weaver Nik,A prime C *-algebra that is not primitive, J. Funct. Anal.,203 (2003), 356–361.
Widom H.,Embedding in algebras of type I, Duke Math. J.,23 (1956), 309–324.
Wright F. B.,A reduction for algebras of finite type, Ann. of Math.,60 (1954), 560–570.
Wright J. D. M.,Wild AW *-factors and Kaplansky-Rickart algebras, J. London Math. Soc.,13 (1976), 83–89.
Zhang L. C.,The proof of inseparable AW *-algebras being primitive C*-algebras, Acta Math. Sinica, english series,19 (2003), 413–416.
Zsido L.,Topological decompositions of W *-algebras I, II, Stud. Cerc. Mat.,25 (1973), 859–945; ibid. Zsido L.,Topological decompositions of W *-algebras I, II, Stud. Cerc. Mat., 25 (1973), 1037–1112.
Raeburn I., Williams D. P.,Morita equivalence and continuous-trace C *-algebras, Mathematical Surveys and Monographs, 60 American Mathematical Society, Providence, RI, 1998.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Saitô, K. OnC *-algebras whose Glimm ideals are primitive. Rend. Circ. Mat. Palermo 56, 251–272 (2007). https://doi.org/10.1007/BF03031444
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03031444