✦ LIBER ✦
On a Question of Pietsch about Hilbert–Schmidt Multilinear Mappings
✍ Scribed by Mário C. Matos
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 120 KB
- Volume
- 257
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
In 1983, Pietsch asked if, for n ≥ 3 and all Hilbert spaces E 1 E n , the vector space of the scalar valued absolutely r r 1 r n -summing multilinear mappings on E 1 × • • • × E n coincides with the vector space of the n-linear Hilbert-Schmidt functionals on
We show that the answer to this question is no. Moreover, we show that the same question, for n ≥ 2 and mappings with values in infinite dimensional Hilbert spaces, has the answer no.