摘要：The concepts of the uncountable K-Bessel and K-Hilbert systems in nonseparable Banach spaces are introduced in this work. The definition for uncountable unconditional basis is given and the criterion for uncountable unconditional basicity is found. Banach space of systems of scalars K is considered and the concepts of K-Bessel and K-Hilbert systems with respect to this space are introduced in nonseparable Banach spaces. K-Besselianness and K-Hilbertianness criteria for a system are found. K-Besselianness and K-Hilbertianness of a system are studied in case where the space K is generated by an uncountable unconditional basis. Non-separable Banach spaces L V p (R) and lp(R) (1 ≤ p < ∞) are constructed. It is shown that in case p ≥ 2 the system e iαt α∈R is lp(R)-Besselian, and in case p ≤ 2 it is lp(R)-Hilbertian in L V p (R).
