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.
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.
We give a brief survey of recent results of order limited operators related to some properties on Banach lattices.
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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