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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
Article

Summary

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.

Keyword

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

Riassunto

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.

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Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

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

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