Locally convex spaces and Schur type properties

We extend Rosenthal's characterization of Banach spaces with the Schur property to a wide class of locally convex spaces (lcs) strictly containing the class of Fr\'{e}chet spaces by showing that for an lcs $E$ from this class the following conditions are equivalent: (1) $E$ has the Schur property, (2) $E$ and $E_w$ have the same sequentially compact sets, where $E_w$ is the space $E$ with the weak topology, (3) $E$ and $E_w$ have the same compact sets, (4) $E$ and $E_w$ have the same countably compact sets, (5) $E$ and $E_w$ have the same pseudocompact sets, (6) $E$ and $E_w$ have the same functionally bounded sets, (7) every bounded non-precompact sequence in $E$ has a subsequence which is equivalent to the unit basis of $\ell_1$. We show that for a quasi-complete lcs conditions (3)-(6) are equivalent to (8) every non-precompact bounded subset of $E$ has an infinite subset which is discrete and $C$-embedded in $E_w$. We prove that every locally convex space is a quotient space of an lcs $E$ satisfying conditions (1)-(5).