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Square roots of perturbed subelliptic operators on Lie groups

Lashi Bandara, A. F. M. ter Elst, Alan McIntosh (2013)

Studia Mathematica

We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower order terms. In this general setting we deduce inhomogeneous estimates. In case the group is nilpotent and the subelliptic operator is pure second order, we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates under small...

Squaring a reverse AM-GM inequality

Minghua Lin (2013)

Studia Mathematica

Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

Stabilité du spectre ponctuel d'opérateurs de Toeplitz généralisés

Lioudmila Nikolskaia (1995)

Studia Mathematica

A general scheme based on a commutation relation is proposed to give rise to a definition of generalized Toeplitz operators on a Banach space. Under suitable conditions the existence of a symbol is proved and its continuation to algebras generated by generalized Toeplitz operators is constructed. A stability theorem for the point spectrum of an operator from generalized Toeplitz algebras is established; as examples one considers the standard and operator valued Toeplitz operators on weighted Hardy...

Stability and boundedness of controllable continuous flows

František Tumajer (1988)

Aplikace matematiky

In the paper the concept of a controllable continuous flow in a metric space is introduced as a generalization of a controllable system of differential equations in a Banach space, and various kinds of stability and of boundedness of this flow are defined. Theorems stating necessary and sufficient conditions for particular kinds of stability and boundedness are formulated in terms of Ljapunov functions.

Stability for non-autonomous linear evolution equations with L p -maximal regularity

Hafida Laasri, Omar El-Mennaoui (2013)

Czechoslovak Mathematical Journal

We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem ( P ) u ˙ ( t ) + A ( t ) u ( t ) = f ( t ) t -a.e. on [ 0 , τ ] , u ( 0 ) = 0 , where A : [ 0 , τ ] → ℒ ( X , D ) is a bounded and strongly measurable function and X , D are Banach spaces such that D → d ↪ X . Our main concern is to characterize L p -maximal regularity and to give an explicit approximation of the problem (P).

Stability of a generalization of the Fréchet functional equation

Renata Malejki (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.

Stability of commuting maps and Lie maps

J. Alaminos, J. Extremera, Š. Špenko, A. R. Villena (2012)

Studia Mathematica

Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.

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