Arbitrary operator A on a Banach space X which is the generator of C0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse theorems on connection between the degree of smoothness of vector x ∈ X with respect to operator A, the rate of convergence to zero of the best approximation ...

The coGalois group associated to a torsion free cover of a Z-module are known to have a canonical topology. In this paper we will see that this topology can be deduced by p-roots of elements of coGalois groups over Zp (p is a prime). We shall investigate in the metric associated to this topology and deduce that the coGalois groups are complete and are isomorphic as metric spaces to products of ...

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C∗-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C∗-subalgebra of M(G)∗ = C0(G) ∗∗. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly com...

Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H∞(X) of bounded holomorph...

We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always w *-continuous on dual operator spaces. For example, this yields a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) ...

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...