On the class of continuous images of non-commutative Valdivia compacta (Q306142)

In [\textit{O. F. K. Kalenda}, Extr. Math. 18, No. 1, 65--80 (2003; Zbl 1159.46306)], the class of continuous images of Corson/Valdivia compact spaces was investigated and several stability results for these classes of spaces were given. The author of this paper non trivially pushes ahead these. Let us recall that a compact space is Valdivia (resp. Corson) if and only if it admits a commutative (resp. full and commutative) retractional skeleton. Here, the class of spaces admitting a retractional skeleton is considered -- in this sense the results of the author are non-commutative analogues of the results of Kalenda. Even though the statements are similar to the commutative case, the proofs are not only straightforward modifications, and additional ideas are needed (e.g. to construct families of retractions). The results are not only generalizations to the non-commutative setting, but even the space of complex-valued functions is considered (in this case, passing from the real case to the complex one requires some additional ideas). Similarly as in the paper by Kalenda mentioned above, certain consequences for nonseparable Banach space theory are collected. Moreover, some relations between Aleksandrov duplicates and retractional skeletons are given.