Lebesgue decomposition theorems

T. Ando, Lebesgue-type decomposition of positive operators, Acta Sci. Math. (Szeged), 38 (1976), 253–260.

N. Dunford and J. Schwarz, Linear operators, Interscience, New York, 1958.

S. P. Gudder, A Radon-Nikodym theorem for *-algebras, Pacific J. Math., 80 (1979), 141–149.

S. Hassi, Z. Sebestyén, H. S. V. De Snoo and F. H. Szafraniec, A canonical decomposition for linear operators and linear relations, Acta Math. Hungar., 115 (2007), 281–307.

S. Hassi, Z. Sebestyén and H. De Snoo, Lebesgue type decompositions for non-negative forms, J. Funct. Anal., 257 (2009), 3858–3894.

T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1980.

F. Riesz and B. Sz.-Nagy, Über Kontraktionen des Hilbertschen Raumes, Acta Sci. Math. (Szeged), 10 (1943), 202–205.

F. Riesz and B. Sz.-Nagy, Leçons d’analyse fonctionnelle, Académie des Sciences de Hongrie, Akadémiai Kiadó, Budapest, 1952.

B. Simon, Lower semicontinuity of positive quadratic forms, Proc. Roy. Soc. Edin., 29 (1977), 267–273.

B. Simon, A canonical decomposition for quadratic forms with applications to monotone convergence theorems, J. Funct. Anal., 28 (1978), 377–385.

ZS. Szűcs, On the Lebesgue decomposition of positive linear functionals, Proc. Amer. Math. Soc., 141 (2013), 619–623.

ZS. Tarcsay, Lebesgue-type decomposition of positive operators, Positivity, OF (2012), DOI: 10.1007/s11117-012-0206-4.

T. Ttkos, Lebesgue decomposition of contents via nonnegative forms, Acta Math. Hungar., OF (2012), DOI: 10.1007/s10474-012-0288-2.

J. Weidmann, Linear operators in Hilbert spaces, Springer-Verlag, Berlin — Heidelberg — New York, 1980.