We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples concerning numerical index, hermitian operators and dissipative operators are also shown.

The existence, uniqueness, regularity and asymptotic behavior of global solutions of semilinear heat equations in Hilbert spaces are studied by developing new results in the theory of one-parameter strongly continuous semigroups of bounded linear operators. Applications to special semilinear heat equations in L(R) governed by pseudo-differential operators are given.

In this paper we establish a relation between the notion of operators of analytic semigroups and matrix transformations from a set of sequences into w∞. We get extensions of some results given by Labbas and de Malafosse concerning applications of the sum of operators in the nondifferential case.

The aim of this paper is to study uniformly elliptic operators with general Wentzell boundary conditions in suitable Lp-spaces by using the approach of sesquilinear forms. We use different tools to re-prove analiticity and related results concerning the semigroups generated by the above operators. In addition, we make some complementary observations on, among other things, compactness issues an...

Some perturbation results for exponentially dichotomous operators are applied to prove the existence of stable and anti-stable solutions of Riccati equations associated to block operators on general Banach spaces, both for compact perturbations and for bisemigroups made up of immediately norm continuous semigroups. r 2003 Elsevier Inc. All rights reserved.

It is shown that if V is a local monoidal pseudovariety of semigroups, then K©m V, D©m V and LI©m V are local. Other operators of the form Z©m( ) are considered. In the process, results about the interplay between operators Z©m( ) and ( ) ∗ Dk are obtained.