  A. Bahramnezhad and K. Haghnejad Azar introduced the classes of
$KB$-operators and $WKB$-operators, and they studied some of theirs properties.
In the present paper, we give answer for an open problem from that paper, which
two classifications of operators, $b$-weakly compact operators and
$KB$-operators are different. A continuous operator $T$ from a normed vectoe
lattice $E$ into a normed space $X$ is said to be $KB$-operator (respectively,
$WKB$-operator) if $\{Tx_n\}_n$ has a norm (respectively, weak) convergent
subsequence in $X$ for every positive increasing sequence $\{x_n\}_n$ in the
closed unit ball $B_E$ of $E$. We investigate some other properties of
$KB$-operators and its relationships with $b-$weakly compact operators.
