The existence of a factorized unbounded operator between Frechet spaces

Creative Commons License

Kizgut E., Yurdakul M.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.13, no.1, 2020 (ESCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1142/s1793557120500175
  • Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Frechet spaces, Kothe spaces, unbounded operators, bounded factorization property
  • Middle East Technical University Affiliated: Yes

Abstract

For locally convex spaces E and F, the continuous linear map T : E -> F is called bounded if there is a zero neighborhood U of E such that T(U) is bounded in F. Our main result is that the existence of an unbounded operator T between Frechet spaces E and F which factors through a third Frechet space G ends up with the fact that the triple (E, G, F) has an infinite dimensional closed common nuclear Kothe subspace, provided that F has the property (y).