BESSAGA CONJECTURE IN UNSTABLE KOTHE SPACES AND PRODUCTS

1993-01-01
NURLU, Z
SARSOUR, J
Let F be a complemented subspace of a nuclear Frechet space E. If E and F both have (absolute) bases (e(n)) resp. (f(n)), then Bessaga conjectured (see [2] and for a more general form, also [8]) that there exists an isomorphism of F into E mapping f(n) to t(n)e(pi(kn)) where (t(n)) is a scalar sequence, pi is a permutation of N, and (k(n)) is a subsequence of N. We prove that the conjecture holds if E is unstable, i.e. for some base of decreasing zero-neighborhoods (U(n)) consisting of absolutely convex sets one has there exists s for-all p there exists q for-all r lim(n) d(n+1)(U(q),U(p)0 / d(n)(U(r),U(s)) = 0 where d(n)(U, V) denotes the nth Kolmogorov diameter.

Citation Formats
Z. NURLU and J. SARSOUR, “BESSAGA CONJECTURE IN UNSTABLE KOTHE SPACES AND PRODUCTS,” STUDIA MATHEMATICA, vol. 104, no. 3, pp. 221–228, 1993, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65548.