Skip to main content
SpringerLink
Log in

Normed algebras with involution

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We show that most of the theory of Hermitian Banach algebras can be proved for normed *-algebras without the assumption of completeness. The conditionr(x)≤p(x) for allx (wherep(x)=r(x * x) 1/2 is the Pták function), which is essential in the theory of Hermitian Banach algebras, is replaced for normed *-algebras by the conditionr(x+y)≤p(x)+p(y) for allx, y. In case of Banach *-algebras these conditions are equivalent.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bonsall F.F. and Duncan J.: Complete normed algebras. Berlin-Heidelberg-New York: Springer 1973

    MATH  Google Scholar 

  2. Doran R.S. and Belfi V.A.: Characterizations ofC * algebras, The Gelfand—Naimark theorems. (Pure and Applied Mathematics) New York-Basel: Marcel Dekker Inc. 1986

    MATH  Google Scholar 

  3. Ford J.W.M.: A square root lemma for Banach star-algebras. J. London Math. Soc. 42, 521–522 (1967)

    MATH  MathSciNet  Google Scholar 

  4. Gelfand I.M. and Naimark M.A.: On the embedding of normed rings into the ring of operators on Hilbert space. Mat. Sbornik 12, 197–213 (1943)

    Google Scholar 

  5. Glimm J.G. and Kadison R.V.: Unitary operators inC *-algebras. Pacific J. Math. 10, 547–556 (1960)

    MATH  MathSciNet  Google Scholar 

  6. Harte R.: Spectral mapping theorems. Proc. Roy. Irish Acad. ser. A 72, 89–107 (1972)

    MATH  MathSciNet  Google Scholar 

  7. Kaplansky I: Symmetry of Banach algebras. Proc. Amer. Math. Soc. 3, 396–399 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  8. Michael E.A.: Locally multiplicately convex topological algebras. Mem. Amer. Math. Soc. No. 11 (1952)

  9. Palmer T.W.: Characterization ofC *-algebras. Bull. Amer. Math. Soc. 74, 538–540 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  10. Pták V: Banach algebras with involution. Manuscripta Math. 6, 245–290 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  11. Russo B. and Dye H.A.: A note on unitary opertors inC *-algebras. Duke Math. J. 33, 413–416 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  12. Shirali S. and Ford J.W.M.: Symmetry in complex involutary Banach algebras. Duke Math. J. 37, 275–280 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  13. Vidav I.: Eine metrische Kennzeichnung der selbstadjungierten Operatoren. Math. Zeitschrift 66, 121–128 (1956)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Czechoslovak Academy of Sciences, Žitná 25, 115 67, Praha 1, Czechoslovakia

    Vladimír Müller

Authors
  1. Vladimír Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research has been supported by a grant from La Junta de Andalucía and by the Department of Applied Mathematics, University of Seville

This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990

Rights and permissions

Reprints and permissions

About this article

Cite this article

Müller, V. Normed algebras with involution. Manuscripta Math 75, 197–210 (1992). https://doi.org/10.1007/BF02567080

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567080

Keywords

Search

Navigation