Bu, Qingying; Shi, Zhongrui On Cohen almost summing multilinear operators. (English) Zbl 1275.47117 J. Math. Anal. Appl. 401, No. 1, 174-181 (2013). The authors introduce and explore the notion of Cohen almost summing multilinear operators. Among other interesting results, it is proved that every Cohen strongly \(p\)-summing multilinear operator \(\left( 1<p\leq \infty\right) \) is Cohen almost summing. The Khinchine inequality plays a crucial role in the proof; this theorem generalizes a linear result from Q.-Y. Bu and P. T. Kranz [J. Math. Anal. Appl. 303, No. 2, 585–590 (2005; Zbl 1071.47025)]. The case of homogeneous polynomials is also investigated. Reviewer: Daniel Pellegrino (João Pessoa) Cited in 1 ReviewCited in 10 Documents MSC: 47H60 Multilinear and polynomial operators 46G25 (Spaces of) multilinear mappings, polynomials 47L22 Ideals of polynomials and of multilinear mappings in operator theory 47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) Keywords:almost summing operators; Cohen strongly summing multilinear operators; multiple summing multilinear operators Citations:Zbl 1071.47025 PDFBibTeX XMLCite \textit{Q. Bu} and \textit{Z. Shi}, J. Math. Anal. Appl. 401, No. 1, 174--181 (2013; Zbl 1275.47117) Full Text: DOI