# Remarks on multiple summing operators on $$C(\Omega )$$ -spaces

Remarks on multiple summing operators on $$C(\Omega )$$ -spaces We give the necessary and sufficient conditions for a multilinear bounded operator on $$C(\Omega _{1}) \times \cdots \times C(\Omega _{k}) \times X_{k+1}\times \cdots \times X_{k+n}$$ to be multiple 1-summing. Based on this result we prove an inclusion result for multiple summing operators and an unexpected composition result of Grothendieck type for bilinear operators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Remarks on multiple summing operators on $$C(\Omega )$$ -spaces

, Volume 18 (1) – Feb 9, 2013
11 pages

/lp/springer_journal/remarks-on-multiple-summing-operators-on-c-omega-spaces-qlTeuhkIe8
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0228-6
Publisher site
See Article on Publisher Site

### Abstract

We give the necessary and sufficient conditions for a multilinear bounded operator on $$C(\Omega _{1}) \times \cdots \times C(\Omega _{k}) \times X_{k+1}\times \cdots \times X_{k+n}$$ to be multiple 1-summing. Based on this result we prove an inclusion result for multiple summing operators and an unexpected composition result of Grothendieck type for bilinear operators.

### Journal

PositivitySpringer Journals

Published: Feb 9, 2013

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