×

zbMATH — the first resource for mathematics

Operator ideals related to absolutely summing and Cohen strongly summing operators. (English) Zbl 1373.47058
Summary: We study the ideals of linear operators between Banach spaces determined by the transformation of vector-valued sequences involving the new sequence space introduced by A. K. Karn and D. P. Sinha [Glasg. Math. J. 56, No. 2, 427–437 (2014; Zbl 1301.46004)] and the classical spaces of absolutely, weakly and Cohen strongly summable sequences. As applications, we prove a new factorization theorem for absolutely summing operators and a contribution to the existence of infinite-dimensional spaces formed by nonabsolutely summing operators is given.

MSC:
47L20 Operator ideals
46B45 Banach sequence spaces
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
PDF BibTeX XML Cite
Full Text: DOI arXiv