Some aspects of \(\lambda (P_0,\mathbb{N})\)-nuclearity (Q2732309)

The author proves a criterion for \(\lambda (P_0 ; \mathbb{N}) \)-nuclearity of generalized Köthe spaces \(\lambda_\mu (P) \) and of locally convex topological vector spaces with generalized bases. NEWLINENEWLINENEWLINEWe recall that, given \(P_0 = \{(b^k_i): k\geq 1 \} \) a stable countable nuclear power set of infinite type, a locally convex space \(E\) with a basis \(U_0\) of absolutely convex neighborhoods of zero is said to be \(\lambda (P_0 ; \mathbb{N}) \)-nuclear if for every \(k\geq 1 \) and \(U \in U_0 \) there exists \(V \in U_0 \) (\(V\subset U\)) such that \( (b^k_i d_i (V,U)) \in \ell^\infty ,\) where \(d_i (V,U) \) are the Kolmogorov \(i\)-diameters.