A Lebesgue-type decomposition for non-positive sesquilinear forms

Abstract

Sesquilinear forms which are not necessarily positive may have a different behavior, with respect to a positive form, on each side. For this reason a Lebesgue-type decomposition on one side is provided for generic forms satisfying a boundedness condition.

An equivalent formulation of 0-closed sesquilinear forms

“…In the last decades, several theorems about the representation (1.2) have been given [1][2][3][4][5]9,11,[13][14][15][16][17]. The topic of the representation is connected to the Lebesgue decomposition (see [6][7][8]12,19]) as motivated in [8].…”

Operators on anti-dual pairs: Lebesgue decomposition of positive operators

“…In the last 50 years quite a number of authors have made significant contributions to the vast literature of non-commutative Lebesgue-Radon-Nikodym theory -here we mention only Ando [2], Gudder [17], Inoue [22], Kosaki [23] and Simon [30], and from the recent past Di Bella and Trapani [7], Corso [8][9][10], ter Elst and Sauter [13], Gheondea [16], Hassi et al [18][19][20][21], Sebestyén and Titkos [32], Szűcs [34], Vogt [46].…”