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Weighted (LF)-spaces of measurable functions

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Abstract

We provide a study for a class of (LF)-spaces where the steps are projective limits of weighted Köthe function spaces. For this class we characterize several regularity conditions in terms of the weights and give a projective description of the inductive limit topology similar as it was done by Bierstedt and Bonet for weighted (LF)-spaces of continuous functions. This extends the work of Reiher on the corresponding (LB)-spaces and generalizes results of Vogt about (LF)-sequence spaces.

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References

  1. K. D. Bierstedt An introduction to locally convex indue titu. limits, pp. 35-133 in Functional Analysis and Applications, Ed. H. Hobge-Nlend, Singapore - New Jersey - Hong Kong (1988).

  2. K. D. Bierstedt, J. Bonet A question of D. Vogt on (LF)-spaces, Arch. Math. (Basel) 61 (1993), 170–172.

    Article  MathSciNet  MATH  Google Scholar 

  3. K. D. Bierstedt, J. Bonet Weighted (LF)-spaces of continuous functions Math. Nachr. 165 (1994), 25–48.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. D. Bierstedt, Ft. Meise, W. H. Summers A projeetive description of weighted inductive limits, Trans. Amer. Math. Soc. 272 (1982), 107–160.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Bonet, C. Fernández Bounded sets in (LF)-spaces, Proc. Amer. Math. Soc. 123 (1995), 3717–3723.

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Frerick, J. Wengenroth Weakly acyclic (LF)-spaces, in: Functional Analysis, Proceedings of the First Workshop at Trier University, S. Dierolf, S. Dineen, P. Domański (eds.), de Gruyter,169-177.

  7. V. P. Palamodov Homological methods in the theory of locally convex spaces, Russian Math. Surveys 26 (1971), 1–64. aiu][8]_P. Pérez Carreras, J. Bonet Barrelled Locally Convex Spaces, North-Holland Math. Studies 131 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  8. K. Reiher Weighted inductive and projeetive limits of normed Köthe function spaces, Results Math. 13 (1988), 147–161.

    Article  MathSciNet  MATH  Google Scholar 

  9. V.S. Retakh Subspaces of a countable inductive limit (Russian), Dokl. Akad. Nauk SSSR 194 (1970), No. 6, English transi. Soviet Math. Dokl. 11 (1970), 1384–1386.

    MATH  Google Scholar 

  10. D. Vogt Regularity properties of (LF)-spaces, pp.57-84 in Progress in Functional Analysis, North-Holland Math. Studies 170 (1992).

  11. J. Wengenroth Acyclic inductive spectra of Fréchet spaces, Studia Math. 120 (1996), 247–258.

    MathSciNet  MATH  Google Scholar 

  12. J. Wengenroth Retractive (LF)-spaces, Dissertation, Universität Trier (1995).

  13. A. C. Zaanen Integration, North-Holland Publ. Co., Amsterdam (1967).

    MATH  Google Scholar 

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  1. FB IV — Mathematik, Universität Trier, D - 54286, Trier, Germany

    Jochen Wengenroth

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  1. Jochen Wengenroth
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Wengenroth, J. Weighted (LF)-spaces of measurable functions. Results. Math. 32, 169–178 (1997). https://doi.org/10.1007/BF03322536

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