Some results of operator ideals on s-type $|A, p|$ operators

Main Article Content

AMIT MAJI
P. D. Srivastava

Abstract

Let $s=(s_{n})$ be a sequence of $s$-numbers in the sense of Pietsch and $A$ be an infinite matrix. This paper presents a generalized class $\mathscr{A}^{(s)}-p$ of $s$-type $|A, p|$ operators using $s$-number sequence which unifies many earlier well known classes. It is shown that the class $\mathscr{A}^{(s)}-p$ forms a quasi-Banach operator ideal under certain conditions on the matrix $A$. Moreover, the inclusion relations among the operator ideals as well as the inclusion relations among their duals are established. It is also proved that for the Ces$\grave{\rm{a}}$ro matrix of order $1$, the operator ideal formed by approximation numbers is small for $1<p< \infty$.

Article Details

How to Cite
MAJI, A., & Srivastava, P. D. (2014). Some results of operator ideals on s-type $|A, p|$ operators. Tamkang Journal of Mathematics, 45(2), 119–136. https://doi.org/10.5556/j.tkjm.45.2014.1297
Section
Papers
Author Biographies

AMIT MAJI

Department ofMathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, West Bengal, India.

P. D. Srivastava

Department ofMathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, West Bengal, India.

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