On monotone extension of linear continuous functionals
نویسندگان
چکیده
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on the effect of linear & non-linear texts on students comprehension and recalling
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15 صفحه اولComputable Jordan Decomposition of Linear Continuous Functionals on $C[0;1]$
By the Riesz representation theorem using the Riemann-Stieltjes integral, linear continuous functionals on the set of continuous functions from the unit interval into the reals can either be characterized by functions of bounded variation from the unit interval into the reals, or by signed measures on the Borel-subsets. Each of these objects has an (even minimal) Jordan decomposition into non-n...
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In this paper, we prove that the integral functional F [u] : BV( ; Rm) → R defined by F [u] := ∫ f (x, u(x),∇u(x)) dx + ∫ ∫ 1 0 f ∞ ( x, u (x), dDsu d|Dsu| (x) ) dθ d|Dsu|(x) is continuous over BV( ; Rm), with respect to the topology of area-strict convergence, a topology in which (W1,1 ∩ C∞)( ; Rm) is dense. This provides conclusive justification for the treatment of F as the natural extension...
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Abstract. Let B(H) be the space of bounded operators on a notnecessarily-separable Hilbert space H . Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T 〈Tx, y〉. We also prove that the identification of weakand strong-operator continuous linear functionals on B(H) cannot be esta...
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ژورنال
عنوان ژورنال: Теория вероятностей и ее применения
سال: 2001
ISSN: 0040-361X
DOI: 10.4213/tvp3830