0000000001275507
AUTHOR
A Trombetta
An extension of Guo's theorem via k-psi-contractive retraction
Let X be a infinite-dimensional Banach space. We generalize Guo''s Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k-ψ-contractions and condensing mappings, under a condition which depends on the infimum kψ of all k \ge1 for which there exists a k-ψ-contractive retraction of the closed unit ball of the space X onto its boundary.
On the admissibility of the space L_{0}(A, X) of vector-valued measurable functions
We prove the admissibility of the space L_0(A,X) of vector-valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets.