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The separable quotient problem for (LF)_tv-spaces

Wieslaw Sliwa
대한수학회 (The Korean Mathematical Society)|2009.11|대한수학회지 (Journal of the KMS)|제46권 제6호|pp. 1233-1242

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참고문헌

키워드

F-spaces(LF)_tv-spacesseparable quotients
주제분류수학

초록

In 1981 S. A. Saxon and P. P. Narayanaswami ([10]) showed that every (LF)-space has an infinite dimensional separable quotient. In this note we prove that this fails for (LF)_tv-spaces. We construct a wide class of (LF)_tv-spaces, which have no infinite dimensional separable quotient.

Abstract

In 1981 S. A. Saxon and P. P. Narayanaswami ([10]) showed that every (LF)-space has an infinite dimensional separable quotient. In this note we prove that this fails for (LF)_tv-spaces. We construct a wide class of (LF)_tv-spaces, which have no infinite dimensional separable quotient.

참고문헌 (14)

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  7. A. M. Plichko, "Symmetric function spaces on atomless probability spaces", Dissertationes Math., 306, pp.85~ (1990)
  8. M. M. Popov, "Codimension of subspaces of Lp(μ) for p < 1", Funktsional. Anal. i Prilozhen., 18(2), pp.94~95 (1984)
  9. H. P. Rosenthal, "On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from Lp (μ) to Lr (º)", J. Functional Analysis, 4, pp.176~214 (1969)
  10. S. A. Saxon, "Metrizable (LF)-spaces, (db)-spaces, and the separable quotient problem", Bull. Austral. Math. Soc., 23(1), pp.65~80 (1981)
  11. spaces, "Studia Math.", 1989, 1~16
  12. W. ´Sliwa, "The separable quotient problem for symmetric function spaces", Bull. Polish Acad. Sci. Math., 48(1), pp.13~27 (2000)
  13. M. Valdivia, "Metrizable (LF)-spaces", Collect. Math., 33(3), pp.299~303 (1982)
  14. A. Wilansky, "Modern Methods in Topological Vector Spaces", McGraw-Hill Inc. (1978)

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