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
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Junek, H.: On dual spaces of locally convex spaces defined by operator ideals, Serd. bulg. math. publ. 3 (1977), 227–235.
Junek, H.: Factorization of linear operators mapping (DF)-spaces into (F)-spaces, Serd. bulg. math. publ. 7 (1981), 372–379.
Junek, H.: Factorization of operators mapping (F)-spaces into (DF)-spaces, (to appear in Ztschr. f. Anal. u. Anw.).
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).
Nelimarkka, E.: The approximation property and locally convex spaces defined by the ideal of approximable operators, (to appear).
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
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