ACTA issues

Lebesgue decomposition theorems

Zoltán Sebestyén, Zsigmond Tarcsay, Tamás Titkos

Acta Sci. Math. (Szeged) 79:1-2(2013), 219-233

Abstract. In the present paper we offer an operator theoretic proof of the Lebesgue decomposition theorem among nonnegative forms on (real or complex) vector spaces. The basic tool in our treatment is the embedding operator between two auxiliary Hilbert spaces associated to the forms in question. As an application of our approach, we also provide the Lebesgue decomposition theorem among finitely additive bounded set functions on rings of sets.

AMS Subject Classification (1991): 47A07; 46N99

Keyword(s): Lebesgue decomposition, nonnegative forms, absolute continuity, singularity, Hilbert space methods

Received November 29, 2012. (Registered under 102/2012.)