The Order Properties of r–compact Operators on Banach Lattices

Banach lattices of L-weakly and M-weakly compact operators

“…, and T n − T r → 0, then give that each T n has a modulus in L r (E, F ), then Theorem 2.1 of [5] tells us that T has a modulus in L r (E, F ) and that…”

A version of Kalton’s theorem for the space of regular operators

“…Case (i) follows by ( [12], Theorem 4.9 ) and case (ii) follows by ( [25], Proposition 2.8). Note also that in case (ii) we also have that K r (E, F ) is a band in L r (E, F ) by ( [11], Theorem 3.7).…”

“…(v) ⇒ (i) By Theorem 2.7, E * and F are KB-spaces. By ( [11], Theorem 2.8), K r (E, F ) has an order continuous norm. Therefore since K r (E, F ) = L r (E, F ), we have that ℓ ∞ is not embeddable in L r (E, F ).…”

L- ve M-zayıf Kompakt Operatörlerin Sıra Yapısı Üzerine

“…Örneğin, [6] 'da her bir ∀ ∈ N için tanımlanan : Aşağıdaki önerme [6], Theorem 3.7 'ye benzer olarak ( , ) ve ( , ) 'nin band olduğu bir durumu belirtmektedir.…”