On ideals of \(n\)-homogeneous polynomials on Banach spaces. (English) Zbl 1095.46026

Floret, Klaus

Strantzalos, P. (ed.) et al., Topological algebras with applications to differential geometry and mathematical physics. Proceedings of the Fest-Colloquium in honour of Professor A. Mallios, University of Athens, Athens, Greece, September 16–18, 1999. Athens: University of Athens, Department of Mathematics. 19-38 (2002).

Summary: This is mainly a survey on the basic ideas of a theory of quasi-normed ideals of \(n\)-homogeneous scalar-valued polynomials on Banach spaces. The ideas for this theory stem for a large part from Pietsch’s theory of operator ideals. As new results, a theorem on ultrastability is extended from normed to \(\lambda\)-normed ideals and some ideals of polynomials factoring through \(L_r(\mu)\) are studied.
For the entire collection see [Zbl 1064.46003].

MSC:

46G25	(Spaces of) multilinear mappings, polynomials
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis