On a Barrelled Space of Class ... and Measure Theory.
Completeness criterion of W. Robertson is generalized. Applications to vector valued sequences and to spaces of linear mappings are given.
A complete isomorphic classification is obtained for Köthe spaces such that ; here χ is the characteristic function of the interval [0,∞), the function κ: ℕ → ℕ repeats its values infinitely many times, and . Any of these spaces has the quasi-equivalence property.
Some relations between the James (or non-square) constant J(X) and the Jordan-von Neumann constant , and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are given as an answer to a problem of Gao and Lau [16]. Connections between and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the -constant, which implies that a Banach space with -constant less than 5/4 has the fixed point property.