ON QUASI-DIAGONAL ISOMORPHISMS OF INFINITE AND FINITE TYPE DRAGILEV KOTHE SPACES


Sozen Y.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, vol.40, no.5, pp.295-314, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 5
  • Publication Date: 2009
  • Journal Name: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.295-314

Abstract

Let 1 <= a(n) NE arrow infinity, kappa be a function on the set of positive integers into itself and chi denotes the characteristic function of [0, infinity). We consider the Kothe spaces of type D(infinity) (kappa, gamma, alpha) = kappa([a(pn)) where a(pn) = exp([p + gamma(n)chi(p - kappa(n))]a(n)), p is an element of N, gamma(n) >= 1, D(0) (kappa, gamma, alpha) = kappa([a(pn)]) where a(pn) = exp([-1/p + gamma(n)chi(p - kappa(n))]a(n)), p is an element of N, gamma(n) >= 0 and H(infinity) (kappa, gamma, alpha) = kappa([a(pn)]) where a(pn) = exp([p + gamma(n) min(p, kappa(n))]a(n)), p is an element of N, gamma(n) >= 1. We characterize the quasi-diagonal isomorphisms between these type of spaces. Moreover, we show that these spaces are not identical, in the topological sense.