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Complex Riesz Spaces,theory to these complex spaces. Recall first that the Cartesian product . × . of the non-empty sets . and . is the set of all ordered pairs (., .) such that . ∈ . and . ∈ .. In the case that . = . = ., where . is a real vector space, we can equip the Cartesian product . × . with a vector space strucContracture 发表于 2025-3-22 11:32:17
The Riesz-Fischer Property and Order Continuous Norms,gent series in . is convergent in norm. More precisely, . is a Banach space if and only if it follows from . ‖.‖ < ∞ (all . in .) that the partial sums .= . . have a norm limit in . (as . → ∞). The norm limit is then often written as . (as we did in section 14), but this may cause confusion if . = .适宜 发表于 2025-3-22 14:34:23
Linear Operators,also called a . or a .) if.for all . and . in . and all (real or complex) numbers . and .. For brevity we shall usually say operator instead of linear operator. It is evident that the set . (.) of all operators from . into . is a vector space if, for ., . in . ( .) and . real or complex, we define .泥沼 发表于 2025-3-22 20:59:03
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