×

On Cohen almost summing multilinear operators. (English) Zbl 1275.47117

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.

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.)

Citations:

Zbl 1071.47025
PDFBibTeX XMLCite
Full Text: DOI