Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On inductive limits of certain $ C\sp *$-algebras of the form $ C(X)\otimes F$

Author: Cornel Pasnicu
Journal: Trans. Amer. Math. Soc. 310 (1988), 703-714
MSC: Primary 46L05; Secondary 46M10
MathSciNet review: 929238
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A certain class of $ {\ast}$-homomorphisms $ C(X) \otimes A \to C(Y) \otimes B$, called compatible with a map defined on $ Y$ with values in the set of all closed nonempty subsets of $ X$, is studied. A local description of $ {\ast}$-homomorphisms $ C(X) \otimes A \to C(Y) \otimes B$ is given considering separately the cases $ X = {\text{point}}$ and $ A = {\mathbf{C}}$; this is done in terms of continuous "quasifields" of $ {C^{\ast}}$-algebras. Conditions under which an inductive limit $ \underrightarrow {\lim }(C({X_k}) \otimes {A_k},\,{\Phi _k})$, where each $ {\Phi _k}$ is of the above type, is $ {\ast}$-isomorphic with the tensor product of a commutative $ {C^{\ast}}$-algebra with an AF algebra are given. For such inductive limits the isomorphism problem is considered.

References [Enhancements On Off] (What's this?)

  • [1] M. Dădârlat, On homomorphisms of certain $ {C^{\ast}}$-algebras, Preprint.
  • [2] -, Inductive limits of $ {C^{\ast}}$-algebras related to some coverings, Preprint.
  • [3] J. Dixmier, Les $ {C^{\ast}}$-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. MR 0171173 (30:1404)
  • [4] E. G. Effros, Dimensions and $ {C^{\ast}}$-algebras, CBMS Regional Conf. Ser. in Math., no. 46, Amer. Math. Soc., Providence, R.I., 1981. MR 623762 (84k:46042)
  • [5] -, On the structure of $ {C^{\ast}}$-algebras: Some old and some new problems, Operator Algebras and Applications, Proc. Sympos. Pure Math., vol. 38, part 1, Amer. Math. Soc., Providence, R.I., 1982, pp. 19-34.
  • [6] J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233-280. MR 0164248 (29:1547)
  • [7] F. Hirzebruch, Topological methods in algebraic geometry, Springer-Verlag, Berlin and New York, 1966. MR 0202713 (34:2573)
  • [8] C. Pasnicu, On certain inductive limit $ {C^{\ast}}$-algebras, Indiana Univ. Math. J. 35 (1986), 269-288. MR 833394 (87k:46118)
  • [9] -, Tensor products of Bunce-Deddens algebras, Operators in Indefinite Metric Spaces, Scattering Theory and Other Topics, Birkhäuser-Verlag, 1987, pp. 283-288. MR 903079 (89a:46125)
  • [10] K. Thomsen, Inductive limits of homogeneous $ {C^{\ast}}$-algebras, Preprint.
  • [11] -, On the diagonalization of matrices over $ C(X)$, Preprint.
  • [12] -, Approximately trivial homogeneous $ {C^{\ast}}$-algebras, Preprint.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L05, 46M10

Retrieve articles in all journals with MSC: 46L05, 46M10

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society