Operator ideals related to absolutely summing and Cohen strongly summing operators. (English) Zbl 1373.47058

Botelho, Geraldo; Campos, Jamilson R.; Santos, Joedson

Pac. J. Math. 287, No. 1, 1-17 (2017).

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.)

Keywords:

Banach sequence spaces; operator ideals; summing operators