In this paper, we introduce and study new concepts of order L-weakly M-weakly compact operators. As consequences, obtain some characterizations Banach lattices with continuous norms or whose topological duals have norms. It is proved that if $$T:E \longrightarrow F$$ an operator between two lattices, then T only its adjoint $$T'$$ compact. Also, show compact, Some related results are also obtai...

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.