In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures Mba(Σ,L(X,Y )). This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures Mba(Σ,L1(X,Y )). This result has interesting applications in optim...

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...

We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternio...

A Banach space X has the approximation property if and only if every compact set in X is in the range of a one-to-one bounded linear operator from a space that has a Schauder basis. Characterizations are given for Lp spaces and quotients of Lp spaces in terms of covering compact sets in X by operator ranges from Lp spaces. A Banach space X is a L1 space if and only if every compact set in X is ...

Let K be an absolutely convex infinite-dimensional compact in a Banach space X . The set of all bounded linear operators T on X satisfying TK ⊃ K is denoted by G(K). Our starting point is the study of the closure WG(K) of G(K) in the weak operator topology. We prove that WG(K) contains the algebra of all operators leaving lin(K) invariant. More precise results are obtained in terms of the Kolmo...

In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operators behave very much like familiar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C : X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X , t...

In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operators behave very much like familiar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C : X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X , t...

The monodromy operator of a linear delay differential equation with periodic coefficients is formulated as an integral operator. The kernel of this operator includes a factor formed from the fundamental solution of the linear delay differential equation. Although the properties of the fundamental solutions are known, in general there is no closed form for the fundamental solution. This paper de...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...