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期刊论文
Extension Theorems of Continuous Random Linear Operators on Random Domains
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 193, 15-27(1995),-0001,():
The central purpose of this paper is to prove the following theorem: let (Ω,σ υ) be a complete probability space, (B, Ⅱ Ⅱ) a normed linear space over the scalar field K, E: Ω-2B a separable random domain with linear subspace values, and f: GrE-K a continuous random linear operator, where GrE={(ω×lq Bx E(ω)} denotes the graph of E. Then there exists a continuous random lin-ear operator f2 Ω×B-K such that f(ω, x)=f(ω, x) A ωΩ, x E(ω), and sup{f(ω, x)Ⅱx B, IIxII≤I}=sup{If(ω, x)Ⅱx E(ω), IIxII≤1}, for each to in 11. For the case where E is not separable, a result similar to the above-stated theorem is also given, which generalizes and improves many previous results on random generalizations of the Hahn-Banach Theorem.
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