Cohen summing multilinear multiplication operators

We give an example of an operator solving in the negative a question of Q. Bu and Z. Shi. Suggested by this example, we find the necessary and sufficient conditions for the multilinear multiplication operator MV:lp1(X1)×⋅⋅⋅×lpk(Xk)→lq(Y) defined byMV((xn1)n∈N,...,(xnk)n∈N)=(Vn(xn1,...,xnk))n∈Nto be...

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Veröffentlicht in:	Journal of mathematical analysis and applications 2021-08, Vol.500 (2), p.125150, Article 125150
1. Verfasser:	Popa, Dumitru
Format:	Artikel
Sprache:	eng
Schlagworte:	Cohen summing operators Multilinear absolutely p-summing operators Multiplication operator Vector valued Banach sequence spaces
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We give an example of an operator solving in the negative a question of Q. Bu and Z. Shi. Suggested by this example, we find the necessary and sufficient conditions for the multilinear multiplication operator MV:lp1(X1)×⋅⋅⋅×lpk(Xk)→lq(Y) defined byMV((xn1)n∈N,...,(xnk)n∈N)=(Vn(xn1,...,xnk))n∈Nto be Cohen p-summing.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2021.125150