We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
We give a brief survey of recent results of order limited operators related to some properties on Banach lattices.
In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.
In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) and f(xσ(y)a)−f(xya)=2f(x)f(y), where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.
We characterize Banach lattices and on which the adjoint of each operator from into which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if and are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator from into has an adjoint Dunford-Pettis operator from into if, and only if, the norm of is order continuous or has the Schur property. As a consequence we show that, if and are two Banach...
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