The mathematical works of Manuel Valdivia. II (Q2760116)

In his paper [in Progress in functional analysis, Proc. Int. Meet. Occas. 60th Birthd. M. Valdivia, Peñíscola/Spain, North-Holland Math. Stud. 170, 1-55 (1992; Zbl 0776.46001], \textit{J. Horváth} had already given a detailed account of the mathematical work of Valdivia up to 1990. The ``International functional analysis meeting on the occasion of the 70th birthday of Professor M. Valdivia'' was held in Valencia, Spain, July 3-7, 2000 (see also Zbl 0971.00063). During the opening ceremony the present author gave an admirable report on the main points of Valdivia's work from 1991 to 1999, and this article is based on the report. We list the headings of the sections (and subsections) of the article to show the various areas (and topics) to which Valdivia made important contributions in the 1990s: Banach spaces (projective resolution of the identity, compact spaces, Markushevich bases, basic sequences, uniform rotundness, direct sum decomposition of spaces), real analyticity (the Borel theorem in real Banach spaces, generalizing the Mityagin results, the Ritt theorem and the interpolation property, domains of real analytic existence), spaces of polynomials and multilinear forms, Fréchet spaces, the Zahorski theorem, infinite-dimensional complex analysis. At the end of the paper, a few words about the mathematician Valdivia are added, and the list of publications is continued (up to number 156 in 1999). \{Reviewer's remarks: In the section on real-analyticity and ultradifferentiable functions, the author takes great care to avoid mentioning his own name. For example, he even writes ``M. Valdivia has considered in [132] and [136]'', but a look at the references reveals that J. Schmets was a co-author of both publications.\}.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00063].