Glasnik Matematicki, Vol. 42, No.2 (2007), 401-409.

MORPHISMS OF EXTENSIONS OF HILBERT C*-MODULES

Biserka Kolarec

Department of Informatics and Mathematics, Faculty of Agriculture, University of Zagreb, Svetošimunska cesta 25, 10000 Zagreb, Croatia
e-mail: bkudelic@agr.hr

Abstract.   We consider the condition for a morphism of (between) extensions of Hilbert C*-modules to exist and give the description of a morphism out of an extension of a Hilbert C*-module in a general case.

2000 Mathematics Subject Classification.   46C50, 46L08.

Key words and phrases.   Hilbert C*-module, morphism, extension, idealizer.

Full text (PDF) (free access)

DOI: 10.3336/gm.42.2.13

References:

  1. W. Arveson, Notes on extensions of C*-algebras, Duke Math. J. 44 (1977), 329-355.
    MathSciNet     CrossRef

  2. D. Bakic, B. Guljas, On a class of module maps of Hilbert C*-modules, Math. Commun. 7 (2002), 177-192.
    MathSciNet

  3. D. Bakic, B. Guljas, Extensions of Hilbert C*-modules, Houston J. Math. 30 (2004), 537-558.
    MathSciNet

  4. D. Bakic, B. Guljas, Extensions of Hilbert C*-modules II, Glas. Mat. Ser. III 38 (2003), 341-357.
    MathSciNet     CrossRef

  5. D. Bakic, Tietze extension theorem for Hilbert C*-modules, Proc. Amer. Math. Soc. 133 (2005), 441-448.
    MathSciNet     CrossRef

  6. L. G. Brown, R. G. Douglas, P. A. Fillmore, Unitary equivalence modulo the compact operators and extensions of C*-algebras, Lecture Notes in Mathematics 345, Springer-Verlag, 1973, 58-128.
    MathSciNet

  7. R. C. Busby, Double cenralizers and extensions of C*-algebras, Trans. Amer. Math. Soc. 132 (1968), 79-99.
    MathSciNet     CrossRef

  8. S. Eilers, T. A. Loring, G. K. Pedersen, Morphisms of extensions of C*-algebras: Pushing forward the Busby invariant, Adv. Math 147 (1999), 74-109.
    MathSciNet     CrossRef

  9. B. Kolarec, Morphisms out of a split extension of a Hilbert C*-module, Glas. Mat. Ser. III 41 (2006), 309-315.
    MathSciNet     CrossRef

  10. E. C. Lance, Hilbert C*-modules - a toolkit for operator algebraists, Lecture Note Series 210, Cambridge University Press, 1995.
    MathSciNet

  11. S. MacLane, Categories for the Working Mathematician, Graduate Texts in Math., vol. 5, Springer-Verlag, 1971.
    MathSciNet

  12. T. A. Loring, Lifting Solutions to Perturbing Problems in C*-algebras, Fields Institute Monographs, 1997.
    MathSciNet

  13. G. K. Pedersen, Extensions of C*-algebras, preprint.

  14. G. K. Pedersen, Pullback and pushout construction in C*-algebra theory, J. Funct. Anal. 167 (1999), 143-344.
    MathSciNet     CrossRef

Glasnik Matematicki Home Page