An asymptotic version of the Gowers dichotomy and a new proof of Wagner theorem (Q331750)

Gowers' dichotomy theorem [\textit{W. T. Gowers}, Geom. Funct. Anal. 6, No. 6, 1083--1093 (1996; Zbl 0868.46007); Ann. Math. (2) 156, No. 3, 797--833 (2002; Zbl 1030.46005)] was extended by \textit{R. Wagner} to weaker forms of unconditionality: asymptotic unconditionality [Proc. Am. Math. Soc. 124, No. 10, 3089--3095 (1996; Zbl 0868.46013)] and \(\alpha\)-asymptotic unconditionality [Ann. Pure Appl. Logic 111, No. 1--2, 39--60 (2001; Zbl 0994.46005)]. In this paper, the author generalizes Wagner's theorems with a new proof. It is based on \textit{B. Maurey}'s proof of the Gowers dichotomy [Math. Sci. Res. Inst. Publ. 34, 149--157 (1999; Zbl 0935.46016)].