Some properties of pre-quasi operator ideal of type generalized Cesáro sequence space defined by weighted means

• Published in: Open mathematics (Warsaw, Poland) Vol. 17; no. 1; pp. 1703 - 1715
• Main Authors: Bakery, Awad A., Mohammed, Mustafa M.
• Format: Journal Article
• Language: English
• Published: Warsaw De Gruyter 31-12-2019; De Gruyter Poland
• Subjects: 46B70; 47B10; 47L20; Approximation; Banach spaces; Eigenvalues; generalized Cesáro sequence space; Linear operators; Mathematical analysis; numbers; pre-quasi operator ideal; s-numbers; simple Banach space; weighted means
• ISSN: 2391-5455; 2391-5455
• DOI: 10.1515/math-2019-0135

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.