Displaying similar documents to “A universal property of C 0 -semigroups”

On the positivity of semigroups of operators

Roland Lemmert, Peter Volkmann (1998)

Commentationes Mathematicae Universitatis Carolinae

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In a Banach space E , let U ( t ) ( t > 0 ) be a C 0 -semigroup with generating operator A . For a cone K ⊆ E with non-empty interior we show: ( ☆ )     U ( t ) [ K ] ⊆ K ( t > 0 ) holds if and only if A is quasimonotone increasing with respect to K . On the other hand, if A is not continuous, then there exists a regular cone K ⊆ E such that A is quasimonotone increasing, but ( ☆ ) does not hold.

Compacta are maximally G δ -resolvable

István Juhász, Zoltán Szentmiklóssy (2013)

Commentationes Mathematicae Universitatis Carolinae

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It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum X contains Δ ( X ) many pairwise disjoint dense subsets, where Δ ( X ) denotes the minimum size of a non-empty open set in X . The aim of this note is to prove the following analogous result: Every compactum X contains Δ δ ( X ) many pairwise disjoint G δ -dense subsets, where Δ δ ( X ) denotes the minimum size of a non-empty G δ set in X .

Inverses of generators of nonanalytic semigroups

Ralph deLaubenfels (2009)

Studia Mathematica

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Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup e t A t ≥ 0 . It is shown that A - 1 generates an O ( 1 + τ ) A ( 1 - A ) - 1 -regularized semigroup. Several equivalences for A - 1 generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of e t A t ≥ 0 , on subspaces, for A - 1 generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate...