On the positive weak almost limited operators

Order Almost Dunford-Pettis Operators on Banach Lattices

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

Weak Banach-Saks property in the space of compact operators

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

Duality Property for Positive Weak Dunford-Pettis Operators

On weak orbits of operators

Let T be a completely nonunitary contraction on a Hilbert space H with r(T ) = 1. Let an > 0, an → 0. Then there exists x ∈ H with |〈Tnx, x〉| ≥ an for all n. We construct a unitary operator without this property. This gives a negative answer to a problem of van Neerven. Let X be a complex Banach space. Then each operator T ∈ B(X) has orbits that are ”large” in the following sense [M1], [B]: Let...

Remarks on Hyponormal Operators and Almost Normal Operators

In 1984 M. Putinar proved that hyponormal operators are subscalar operators of order two. The proof provided a concrete structure of such operators. We will use this structure to give a sufficient condition for hyponormal operators T with trace-class commutator to admit a direct summand S so that T ⊕ S is the sum of a normal operator and a HilbertSchmidt operator. We investigate what this suffi...