Let $s=(s_{n})$ be a sequence of $s$-numbers in the sense of Pietsch and $A$ be an infinite matri... more 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
Let $s=(s_{n})$ be a sequence of $s$-numbers in the sense of Pietsch and $A$ be an infinite matri... more 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
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Papers by Amit Maji