# Strictly singular operator

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In functional analysis, a branch of mathematics, a **strictly singular operator** is a bounded linear operator *L* from a Banach space *X* to another Banach space *Y*, such that it is not an isomorphism, and fails to be an isomorphism on any infinite dimensional subspace of *X*. Any compact operator is strictly singular, but not vice-versa.^{[1]}^{[2]}

Every bounded linear map , for , , is strictly singular. Here, and are sequence spaces. Similarly, every bounded linear map and , for , is strictly singular. Here 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.