(p, q)-Summing Sequences of Operators
| Autor: | Arregui, Jose Luis, Blasco, Oscar |
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| Zdroj: | Quaestiones Mathematicae; December 2003, Vol. 26 Issue: 4 p441-452, 12p |
| Abstrakt: | A sequence (uj)j∈N of operators inL (X, Y) is a (p, q)-summing multiplier (or (p, q)-summing sequence of operators), in short (uj) ∈lπp, q (X, Y), if there exists a constant C > 0 such that, for any finite collection of vectors x1, x2,... xn in X, it holds that(nΣj=1||ujxj||p)1/p≤ C sup {(nΣj=1|x*xj|q)1/q; x* ∈ BX*}.Some examples of these operators, inclusions between the spaces and connections with spaces of multipliers are presented. |
| Databáze: | Supplemental Index |
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