Skip to main content
SpringerLink
Log in

Normal AW*-Algebras

  • Chapter
Mappings of Operator Algebras

Part of the book series: Progress in Mathematics ((PM,volume 84))

  • 347 Accesses

Abstract

Let us recall that a C*-algebra A is an AW*-algebra if (1) each maximal abelian *-subalgebra of A is generated by its projections and (2) each family of orthogonal projections {e α} in A has a supremum Σ A e α in Proj(A) (the set of all projections in A).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. E. Christensen and G.K. Pedersen, Properly infinite AW*-algebras are monotone sequentially complete, Bull. London Math. Soc., 16 (1984), 407–410.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Hamana, Regular embeddings of C*-algebras in monotone complete C*-algebras, J. Math. Soc. Japan 33 (1981), 159–183.

    Article  MathSciNet  Google Scholar 

  3. I. Kaplansky, Projections in Banach algebras, Ann. of Math., 53 (1951), 235–249.

    Article  MathSciNet  MATH  Google Scholar 

  4. I. Kaplansky, Algebras of type I, Ann. of Math. 56 (1952), 460–472.

    Article  MathSciNet  MATH  Google Scholar 

  5. K. Saitô, On the embedding as a double commutator in a type I AW*-algebra II, Tôhoku Math. J., 26 (1974), 333–339.

    Article  MATH  Google Scholar 

  6. K. Saitô, On normal AW*-algebras, Tôhoku Math. J., 33 (1981), 567–572.

    Article  MATH  Google Scholar 

  7. J.D.M. Wright, Regular σ-completions of C*-algebras, J. London Math. Soc., 12 (1976), 299–309.

    Article  MATH  Google Scholar 

  8. J.D.M. Wright, Normal AW*-algebras, Proc. Roy. Soc. Edinburgh 85A (1980), 137–141.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, Tôhoku University, Sendai, Japan

    Kazuyuki Saitô

  2. Dept. of Mathematics, University of Reading, Whiteknights, Reading, UK

    J. D. M. Wright

Authors
  1. Kazuyuki Saitô
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. D. M. Wright
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Huzihiro Araki

  2. Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania, USA

    Richard V. Kadison

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Saitô, K., Wright, J.D.M. (1991). Normal AW*-Algebras. In: Araki, H., Kadison, R.V. (eds) Mappings of Operator Algebras. Progress in Mathematics, vol 84. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0453-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0453-4_19

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6767-6

  • Online ISBN: 978-1-4612-0453-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation