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Linear operators in (F) - spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 991)

Abstract

A theorem concerning the factorization of operators in (F)-spaces through Banach spaces and Banach ideals is presented. The theorem is used to investigate the relation between the bornological and the geometric topological structure of operators and of (F)-spaces.

Keywords

  • Banach Space
  • Operator Ideal
  • Convex Space
  • Factorization Theorem
  • Linear Continuous Operator

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References

  1. Grothendieck, A.: Sur les espaces (F) et (DF), Summa Brasil Math. vol 3, fasc. 6 (1954), 57–121.

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  2. Junek, H.: On dual spaces of locally convex spaces defined by operator ideals, Serd. bulg. math. publ. 3 (1977), 227–235.

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  3. Junek, H.: Factorization of linear operators mapping (DF)-spaces into (F)-spaces, Serd. bulg. math. publ. 7 (1981), 372–379.

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  4. Junek, H.: Factorization of operators mapping (F)-spaces into (DF)-spaces, (to appear in Ztschr. f. Anal. u. Anw.).

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  5. Nelimarkka, E.: On operator ideals and locally convex A-spaces with applications to λ-nuclearity, Thesis, Ann. Acad. Scient. Fenn., series A, Math. Diss. 13 (1977).

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  6. Nelimarkka, E.: The approximation property and locally convex spaces defined by the ideal of approximable operators, (to appear).

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  7. Pietsch, A.: Operator Ideals, Berlin 1978.

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© 1983 Springer-Verlag

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Junek, H. (1983). Linear operators in (F) - spaces. In: Pietsch, A., Popa, N., Singer, I. (eds) Banach Space Theory and its Applications. Lecture Notes in Mathematics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061565

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  • DOI: https://doi.org/10.1007/BFb0061565

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12298-2

  • Online ISBN: 978-3-540-39877-6

  • eBook Packages: Springer Book Archive