Abstract. In 1975, Rhoades [9] generalized the classes of, operators of l_p type and operators of Cesaro type by introducing an arbitrary infinite matrix A = (a_nk) using approximation numbers of a bounded linear operator. In the same paper Rhoades has proved that for each fixed matrix A satisfying the condition |a_{n, 2k-1}| + |a_{n, 2k}| ≤ M|a__nk| on the matrix A = (a_nk) for each n, k = 1, 2, ... and each p, 0 < p ≤ ∞ the set A-p type operators is a linear space and raised an open question whether this condition is necessary to be a linear space? In this paper we have answered the question in negation. Further, we have introduced and studied the class A^(s)-p of s-type ces_p operators using s-number sequence and Cesaro sequence spaces. We have also shown that the class A^^(s)-p forms a quasi-Banach operator ideal. Moreover, the inclusion relations among the operator ideals are established.

Received: January 10, 2013

AMS Subject Classification: 47B06, 47L20

Key Words and Phrases: -numbers, approximation numbers, operator ideals, sequence space

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