SCHATTEN-TYPE CLASSES ON SEQUENCE SPACES
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Abstract
Let $H$ be a Hilbert space and $L(H)$ be the bounded linear operators on $H$. For $T\in L(H)$, let
$$||T||_P=\sup\left[\sum_{n=1}^\infty|<Te_n, e_n>|^p\right]^{1/p},$$
where the supremum is taken over all orthonormal sequences $(e_n)$. Set $C_p(H)=\{T\in L(H) : ||T||_p<\infty\}$. The object of this paper is to define and study $C_p(X , Y)$ where $X$ and $Y$ are sequences spaces
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