On a problem by Arens, Goldberg, and Luxemburg

Details On a problem by Arens, Goldberg, and Luxemburg On a problem by Arens, Goldberg, and Luxemburg

2002-12-05

arxiv.org/abs/math/0212075v1

Mathematics

Functional Analysis

7 pages, 2 pictures, submitted, Pacific J. Math

Scientific paper

We construct a normed algebra ${\calA}$ with norm $N(\cdot)$ over the reals,
which is {\em quadrative} in the sense that $N(A^2) \le N(A)^2$ for all $A \in
{\cal A}$, but is not 3-{\em bounded} in the sense that $N(A^3) \le N(A)^3$.
This answers a question of Arens, Goldberg, and Luxemburg.

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