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...

Analytic semigroups on vector valued noncommutative L p -spaces

Cédric Arhancet (2013)

Studia Mathematica

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We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( ( T ⊗ I d E ) t ≥ 0 on the vector valued noncommutative L p -space L p ( M , E ) . Moreover, we give applications to the H ∞ ( Σ θ ) functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

Universal Jamison spaces and Jamison sequences for C₀-semigroups

Vincent Devinck (2013)

Studia Mathematica

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An increasing sequence ( n k ) k ≥ 0 of positive integers is said to be a Jamison sequence if for every separable complex Banach space X and every T ∈ ℬ(X) which is partially power-bounded with respect to ( n k ) k ≥ 0 , the set σ p ( T ) ∩ is at most countable. We prove that for every separable infinite-dimensional complex Banach space X which admits an unconditional Schauder decomposition, and for any sequence ( n k ) k ≥ 0 which is not a Jamison sequence, there exists T ∈ ℬ(X) which is partially power-bounded with respect to ( n k ) k ≥ 0 ...

On the structure of continuous uninorms

Paweł Drygaś (2007)

Kybernetika

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Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation U in the unit interval with the neutral element e ∈ [ 0 , 1 ] . If operation U is continuous, then e = 0 or e = 1 . So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element e ∈ ( 0 , 1 ) , which is continuous in the open unit square may be...