Unstable splittings for real spectra (Q1948309)

Concerning real-oriented cohomology theories see, \textit{S. Araki} [Jap. J. Math., New Ser. 5, 403--430 (1979; Zbl 0443.55003)]. The second author constructed unstable splittings for the \(\Omega\)-spectra \(BP, BP\langle n\rangle\) and \(E(n)\), in [Am. J. Math. 97, 101--123 (1975; Zbl 0303.55003)]. Boardman and second author constructed real-oriented analogs of the above mentioned splittings, \textit{J. Boardman} and \textit{W. Wilson} in [Cohomological methods in homotopy theory. Proceedings of the Barcelona conference on algebraic topology (BCAT), Bellaterra, Spain, June 4-10, 1998. Basel: Birkhäuser. Prog. Math. 196, 35--45 (2001; Zbl 0988.55006)]. Here the authors show how the above mentioned Wilson splittings can be obtained from the above mentioned real-oriented Boardman-Wilson splittings.