Every Banach ideal of polynomials is compatible with an operator ideal

Details Every Banach ideal of polynomials is compatible with an operator ideal Every Banach ideal of polynomials is compatible with an operator ideal

2010-09-06

arxiv.org/abs/1009.1064v1

Monatsh Math (2012) 165:1-14

Mathematics

Functional Analysis

12 pages

Scientific paper

10.1007/s00605-010-0255-3

We show that for each Banach ideal of homogeneous polynomials, there exists a
(necessarily unique) Banach operator ideal compatible with it. Analogously, we
prove that any ideal of $n$-homogeneous polynomials belongs to a coherent
sequence of ideals of $k$-homogeneous polynomials.

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