Abstract
Let
be a generalized Cesáro sequence space defined by weighted means and by using
-numbers of operators from a Banach space
into a Banach space
. We give the sufficient (not necessary) conditions on
such that the components
of the class
form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal
, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small and the pre-quasi Banach operator ideal constructed by
-numbers is simple Banach space. Finally the pre-quasi operator ideal formed by the sequence of
-numbers and this sequence space is strictly contained in the class of all bounded linear operators, whose sequence of eigenvalues belongs to this sequence space.