Adjoint characterisations of quasi-weakly compact linear relations

Quasi-compact Operators in Topological Linear Spaces

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

Some properties of b-weakly compact operators on Banach lattices

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

Relations between Sets of Time Points and Quasi-linear Orderings

Weakly Compact #?-algebras

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

Weakly Compact Groups of Operators

It is shown that the weakly closed algebra generated by a weakly compact group of operators on a Banach space is reflexive and equals its second commutant. Also, an example is given to show that the generator of a monothetic weakly compact group of operators need not have a logarithm in the algebra of all bounded linear operators on the underlying space. Let X be a complex Banach space, B(X) th...