# Strictly singular operator

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Every bounded linear map $T:l_p\to l_q$, for $1\le q, p < \infty$, $p\ne q$, is strictly singular. Here, $l_p$ and $l_q$ are sequence spaces. Similarly, every bounded linear map $T:c_0\to l_p$ and $T:l_p\to c_0$, for $1\le p < \infty$, is strictly singular. Here $c_0$ is the Banach space of sequences converging to zero. This is a corollary of Pitt's theorem, which states that such T, for q < p, are compact.