Radon–Nikodym Theorems for Nonnegative Forms, Measures and Representable Functionals

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• 作者：Zsigmond Tarcsay
• 关键词：Radon–Nikodym theorem ; Absolute continuity ; Set function ; Hermitian form ; Measure
• 刊名：Complex Analysis and Operator Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：10
• 期：3
• 页码：479-494
• 全文大小：478 KB
• 参考文献：1.Darst, R.B., Green, E.: On a Radon–Nikodym theorem for finitely additive set functions. Pac. J. Math. 27, 255–259 (1968)CrossRef MathSciNet MATH
  2.Fefferman, C.: A Radon–Nikodym theorem for finitely additive set functions. Pac. J. Math. 23, 35–45 (1967)CrossRef MathSciNet MATH
  3.Gudder, S.P.: A Radon–Nikodym theorem for \(^*\) -algebras. Pac. J. Math. 80, 141–149 (1979)CrossRef MathSciNet MATH
  4.Hassi, S., Sebestyén, Z., de Snoo, H.: Lebesgue type decompositions for nonnegative forms. J. Funct. Anal. 257, 3858–3894 (2009)CrossRef MathSciNet MATH
  5.Sebestyén, Z.: On representability of linear functionals on \(^*\) -algebras. Period. Math. Hungar. 15, 233–239 (1984)CrossRef MathSciNet MATH
  6.Sebestyén, Z., Tarcsay, Zs., Titkos, T.: Lebesgue decomposition theorems. Acta Sci. Math. (Szeged) 79, 219–233 (2013)
  7.Sebestyén, Z., Titkos, T.: A Radon–Nikodym type theorem for forms. Positivity 17, 863–873 (2013)CrossRef MathSciNet MATH
  8.Simon, B.: A canonical decomposition for quadratic forms with applications to monotone convergence theorems. J. Funct. Anal. 28, 377–385 (1978)CrossRef MathSciNet MATH
  9.Szűcs, Zs.: The Lebesgue decomposition of representable forms over algebras. J. Oper. Theory 70, 3–31 (2013)
  10.Tarcsay, Zs.: Lebesgue-type decomposition of positive operators. Positivity 17, 803–817 (2013)
  11.Titkos, T.: Lebesgue decomposition of contents via nonnegative forms. Acta Math. Hung. 140, 151–161 (2013)CrossRef MathSciNet MATH
  
• 作者单位：Zsigmond Tarcsay (1)
  
  1. Department of Applied Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest, 1117, Hungary
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262

文摘

The aim of this paper is to establish two Radon–Nikodym-type theorems for nonnegative Hermitian forms defined on a real or complex vector space and to apply these results to provide some known Radon–Nikodym-type theorems of the theory of representable positive functionals, \(\sigma \)-additive and finitely additive measures.