Displaying similar documents to “On the K-theory of the C * -algebra generated by the left regular representation of an Ore semigroup”

The algebra of the subspace semigroup of M ( q )

Jan Okniński (2002)

Colloquium Mathematicae

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The semigroup S = S ( M ( q ) ) of subspaces of the algebra M ( q ) of 2 × 2 matrices over a finite field q is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.

On semigroups with an infinitesimal operator

Jolanta Olko (2005)

Annales Polonici Mathematici

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Let F t : t 0 be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small t every linear selection of F t is invertible and there exists an exponential semigroup f t : t 0 of linear continuous selections f t of F t .

A local Landau type inequality for semigroup orbits

Gerd Herzog, Peer Christian Kunstmann (2014)

Studia Mathematica

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Given a strongly continuous semigroup ( S ( t ) ) t 0 on a Banach space X with generator A and an element f ∈ D(A²) satisfying | | S ( t ) f | | e - ω t | | f | | and | | S ( t ) A ² f | | e - ω t | | A ² f | | for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.

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...

Operator theoretic properties of semigroups in terms of their generators

S. Blunck, L. Weis (2001)

Studia Mathematica

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Let ( T t ) be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup S t : = 0 t T s d s belongs to . For analytic semigroups, S t implies T t , and in this case we give precise estimates for the growth of the -norm of T t (e.g. the trace of T t ) in terms of the resolvent growth and the imbedding D(A) ↪ X.

Spaces of multipliers and their preduals for the order multiplication on [0,1]. II

Savita Bhatnagar (2004)

Colloquium Mathematicae

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Consider I = [0,1] as a compact topological semigroup with max multiplication and usual topology, and let C ( I ) , L p ( I ) , 1 p , be the associated algebras. The aim of this paper is to study the spaces H o m C ( I ) ( L r ( I ) , L p ( I ) ) , r > p, and their preduals.

On upper triangular nonnegative matrices

Yizhi Chen, Xian Zhong Zhao, Zhongzhu Liu (2015)

Czechoslovak Mathematical Journal

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We first investigate factorizations of elements of the semigroup S of upper triangular matrices with nonnegative entries and nonzero determinant, provide a formula for ρ ( S ) , and, given A S , also provide formulas for l ( A ) , L ( A ) and ρ ( A ) . As a consequence, open problem 2 and problem 4 presented in N. Baeth et al. (2011), are partly answered. Secondly, we study the semigroup of upper triangular matrices with only positive integral entries, compute some invariants of such semigroup, and also partly answer...

Spaces of multipliers and their preduals for the order multiplication on [0, 1]

Savita Bhatnagar, H. L. Vasudeva (2002)

Colloquium Mathematicae

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Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), L p ( I ) , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise H o m C ( I ) ( L r ( I ) , L p ( I ) ) and their preduals.

Algebra in the superextensions of twinic groups

Taras Banakh, Volodymyr Gavrylkiv

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Given a group X we study the algebraic structure of the compact right-topological semigroup λ(X) consisting of all maximal linked systems on X. This semigroup contains the semigroup β(X) of ultrafilters as a closed subsemigroup. We construct a faithful representation of the semigroup λ(X) in the semigroup ( X ) ( X ) of all self-maps of the power-set (X) and show that the image of λ(X) in ( X ) ( X ) coincides with the semigroup E n d λ ( ( X ) ) of all functions f: (X) → (X) that are equivariant, monotone and symmetric...

Semigroups generated by convex combinations of several Feller generators in models of mathematical biology

Adam Bobrowski, Radosław Bogucki (2008)

Studia Mathematica

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Let be a locally compact Hausdorff space. Let A i , i = 0,1,...,N, be generators of Feller semigroups in C₀() with related Feller processes X i = X i ( t ) , t 0 and let α i , i = 0,...,N, be non-negative continuous functions on with i = 0 N α i = 1 . Assume that the closure A of k = 0 N α k A k defined on i = 0 N ( A i ) generates a Feller semigroup T(t), t ≥ 0 in C₀(). A natural interpretation of a related Feller process X = X(t), t ≥ 0 is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ , with probability...

Non supercyclic subsets of linear isometries on Banach spaces of analytic functions

Abbas Moradi, Karim Hedayatian, Bahram Khani Robati, Mohammad Ansari (2015)

Czechoslovak Mathematical Journal

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Let X be a Banach space of analytic functions on the open unit disk and Γ a subset of linear isometries on X . Sufficient conditions are given for non-supercyclicity of Γ . In particular, we show that the semigroup of linear isometries on the spaces S p ( p > 1 ), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space H p or the Bergman space L a p ( 1 < p < , p 2 )...

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.

L₁-uniqueness of degenerate elliptic operators

Derek W. Robinson, Adam Sikora (2011)

Studia Mathematica

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Let Ω be an open subset of d with 0 ∈ Ω. Furthermore, let H Ω = - i , j = 1 d i c i j j be a second-order partial differential operator with domain C c ( Ω ) where the coefficients c i j W l o c 1 , ( Ω ̅ ) are real, c i j = c j i and the coefficient matrix C = ( c i j ) satisfies bounds 0 < C(x) ≤ c(|x|)I for all x ∈ Ω. If 0 d s s d / 2 e - λ μ ( s ) ² < for some λ > 0 where μ ( s ) = 0 s d t c ( t ) - 1 / 2 then we establish that H Ω is L₁-unique, i.e. it has a unique L₁-extension which generates a continuous semigroup, if and only if it is Markov unique, i.e. it has a unique L₂-extension which generates a submarkovian semigroup....

Hukuhara's differentiable iteration semigroups of linear set-valued functions

Andrzej Smajdor (2004)

Annales Polonici Mathematici

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Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. A family F t : t 0 of continuous linear set-valued functions F t : K c c ( K ) is a differentiable iteration semigroup with F⁰(x) = x for x ∈ K if and only if the set-valued function Φ ( t , x ) = F t ( x ) is a solution of the problem D t Φ ( t , x ) = Φ ( t , G ( x ) ) : = Φ ( t , y ) : y G ( x ) , Φ(0,x) = x, for x ∈ K and t ≥ 0, where D t Φ ( t , x ) denotes the Hukuhara derivative of Φ(t,x) with respect to t and G ( x ) : = l i m s 0 + ( F s ( x ) - x ) / s for x ∈ K.

Rational fixed points for linear group actions

Pietro Corvaja (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove a version of the Hilbert Irreducibility Theorem for linear algebraic groups. Given a connected linear algebraic group G , an affine variety V and a finite map π : V G , all defined over a finitely generated field κ of characteristic zero, Theorem 1.6 provides the natural necessary and sufficient condition under which the set π ( V ( κ ) ) contains a Zariski dense sub-semigroup Γ G ( κ ) ; namely, there must exist an unramified covering p : G ˜ G and a map θ : G ˜ V such that π θ = p . In the case κ = , G = 𝔾 a is the additive group, we...

On the Cauchy problem for convolution equations

(2013)

Colloquium Mathematicae

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We consider one-parameter (C₀)-semigroups of operators in the space ' ( ; m ) with infinitesimal generator of the form ( G * ) | ' ( ; m ) where G is an M m × m -valued rapidly decreasing distribution on ℝⁿ. It is proved that the Petrovskiĭ condition for forward evolution ensures not only the existence and uniqueness of the above semigroup but also its nice behaviour after restriction to whichever of the function spaces ( ; m ) , L p ( ; m ) , p ∈ [1,∞], ( a ) ( ; m ) , a ∈ ]0,∞[, or the spaces L q ' ( ; m ) , q ∈ ]1,∞], of bounded distributions.

Semigroups generated by certain pseudo-differential operators on the half-space 0 + n + 1

Victoria Knopova (2004)

Colloquium Mathematicae

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The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on 0 + n + 1 and study some of their properties. Secondly, we consider the fractional powers of an operator of the form - A ± = - ψ ( D x ' ) ± / ( x n + 1 ) , ( x ' , x n + 1 ) 0 + n + 1 , where ψ ( D x ' ) is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator - ( - A ± ) α and prove that with this domain it generates an L p -sub-Markovian semigroup.

On some free semigroups, generated by matrices

Piotr Słanina (2015)

Czechoslovak Mathematical Journal

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Let A = 1 2 0 1 , B λ = 1 0 λ 1 . We call a complex number λ “semigroup free“ if the semigroup generated by A and B λ is free and “free” if the group generated by A and B λ is free. First families of semigroup free λ ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free λ ’s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common...

H calculus and dilatations

Andreas M. Fröhlich, Lutz Weis (2006)

Bulletin de la Société Mathématique de France

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We characterise the boundedness of the H calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if - A generates a bounded analytic C 0 semigroup ( T t ) on a UMD space, then the H calculus of A is bounded if and only if ( T t ) has a dilation to a bounded group on L 2 ( [ 0 , 1 ] , X ) . This generalises a Hilbert space result of C.LeMerdy. If X is an L p space we can choose another L p space in place of L 2 ( [ 0 , 1 ] , X ) .

Second order elliptic operators with complex bounded measurable coefficients in  L p , Sobolev and Hardy spaces

Steve Hofmann, Svitlana Mayboroda, Alan McIntosh (2011)

Annales scientifiques de l'École Normale Supérieure

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Let  L be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with L , such as the heat semigroup and Riesz transform, are not, in general, of Calderón-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in  L p , Sobolev, and some new Hardy spaces naturally associated to  L . First, we show...