On quasi-contractivity of C0-semigroups on Banach spaces

On Quasi-contractivity of C0-semigroups on Banach Spaces

A basic result in semigroup theory states that every C0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e t n P ) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introd...

C0-semigroups of linear operators on some ultrametric Banach spaces

C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric) free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss...

On c0-saturated Banach spaces

A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. A c0-saturated Banach space with an unconditional basis which has a quotient space isomorphic to l2 is constructed. A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. In [2] and [3], it was asked whether all quotient spaces ...

On quasi-complemented subspaces of banach spaces.

A remark of contraction semigroups on Banach spaces

Let X be a complex Banach space and let J : X → X∗ be a duality section on X (i.e. 〈x, J(x)〉 = ‖J(x)‖‖x‖ = ‖J(x)‖2 = ‖x‖2). For any unit vector x and any (C0) contraction semigroup T = {e tA : t ≥ 0}, Goldstein proved that if X is a Hilbert space and if |〈T (t)x, J(x)〉| → 1 as t → ∞, then x is an eigenvector of A corresponding to a purely imaginary eigenvalue. In this article, we prove the simi...