Il Nuovo Cimento B (1971-1996)

, Volume 94, Issue 2, pp 193–203 | Cite as

The adjoint of an additive map

  • J. Pian
  • C. S. Sharma


It is proved that the mapping which assigns to a bounded additive map from one complex Banach space to another its adjoint is an additive monomorphism. It is shown that differences in the structures of continuous additive maps on a complex Banach space and of linear maps on a real Banach space are not trivial. Certain aspects of the curious rule by which a complex variable and its complex conjugate are treated as independent of each other are discussed.


PACS. 03.65.Db Functional analytical methods PACS. 02.30 Function theory analysis 


Si prova che la mappatura che assegna ad una mappa additiva limitata da uno spazio di Banach complesso ad un altro il suo aggiunto è un monomorfismo additivo. Si mostra che le differenze nelle strutture di mappe additive continue su uno spazio complesso di Banach e di mappe lineari non sono banali. Si discutono certi aspetti della curiosa regola con la quale una variabile complessa e la sua coniugata complessa sono trattate come indipendenti l'una dall'altra.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    C. S. Sharma andI. Rebelo:Int. J. Theor. Phys.,13, 323 (1975).MathSciNetCrossRefGoogle Scholar
  2. (2).
    G. Fonte:Nuovo Cimento B,49, 200 (1979).MathSciNetADSCrossRefGoogle Scholar
  3. (3).
    G. Fonte:J. Math. Phys. (N.Y.),21, 800 (1980).MathSciNetADSCrossRefGoogle Scholar
  4. (4).
    G. Fonte:Lett. Nuovo Cimento,41, 577 (1984).MathSciNetCrossRefGoogle Scholar
  5. (5).
    G. Fonte andG. Schiffrer:Nuovo Cimento B,74, 1 (1983).MathSciNetADSCrossRefGoogle Scholar
  6. (6).
    J. Pian andC. S. Sharma:Phys. Lett. A (Amsterdam),76, 365 (1980).MathSciNetADSGoogle Scholar
  7. (7).
    J. Pian andC. S. Sharma:J. Phys. A (London) 14, 1261 (1981).MathSciNetADSGoogle Scholar
  8. (8).
    J. Pian andC. S. Sharma:Int. J. Theor. Phys.,22, 107 (1983).MathSciNetCrossRefGoogle Scholar
  9. (9).
    J. Pian andC. S. Sharma:Lett. Nuovo Cimento,40, 126 (1984).MathSciNetCrossRefGoogle Scholar
  10. (10).
    E. C. G. Stueckelberg:Helv. Phys. Acta,33, 727 (1960).MathSciNetGoogle Scholar
  11. (11).
    E. C. G. Stueckelberg andM. Guenin:Helv. Phys. Acta,34, 621 (1961).Google Scholar
  12. (12).
    E. C. G. Stueckelberg andM. Guenin:Helv. Phys. Acta,35, 673 (1962).Google Scholar
  13. (13).
    E. C. G. Stueckelberg, M. Guenin, C. Piron andH. Ruegy:Hevl. Phys. Acta,34, 675 (1961).Google Scholar
  14. (14).
    N. Dunford andJ. T. Schwartz:Linear Operators, part I (Interscience, New York, N. Y., 1958).Google Scholar
  15. (15).
    P. Halmos:Introduction to Hilbert Space and the Theory of Spectral Multiplicity (Chelsea, New York, N. Y., 1957).Google Scholar
  16. (16).
    C. S. Sharma:Br. J. Philos. Sci.,33, 275 (1982).CrossRefGoogle Scholar
  17. (17).
    S.-s. Chern:Complex Manifolds without Potential Theory (Springer, Berlin, 1979).CrossRefGoogle Scholar
  18. (18).
    R. O. Wells:Differential Analysis on Complex Manifolds (Springer, Berlin, 1980).CrossRefGoogle Scholar
  19. (19).
    J. Pian:Optimization on Complex Banach Spaces, Ph. D. Thesis (London University, 1981).Google Scholar

Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • J. Pian
    • 1
  • C. S. Sharma
    • 1
  1. 1.Department of MathematicsBirkbeck CollegeLondonEngland

Personalised recommendations