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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Absolutely $(r,p,q)$-summing inclusions

### Tom 178 / 2007

Studia Mathematica 178 (2007), 19-45 MSC: 47B10, 46M35, 47B06. DOI: 10.4064/sm178-1-2

#### Streszczenie

As a continuation of the work of Bennett and Carl for the case $q=\infty$, we consider absolutely $(r,p,q)$-summing inclusion maps between Minkowski sequence spaces, $1 \le p,q \le 2$. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of $(u,s,t)$-nuclear and of absolutely $(r,p,q)$-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary Banach sequence spaces and inclusions between finite-dimensional Schatten classes. Finally, applications to Hilbert numbers of inclusions are given.

#### Autorzy

• Carsten MichelsDepartment of Mathematics
University of Oldenburg
Postfach 2503
D-26111 Oldenburg, Germany
e-mail

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