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Furthermore, our construction also allows to extend G-equivariant completely bounded operators acting on the space part to the crossed-product provided that the generalized Følner sets of the action θ satisfy certain accretivity property.
The stability of delay ordinary differential and difference equations and delay partial differential and difference equations with bounded operators acting on delay terms has been studied extensively in a large cycle of works (see [1 13] and the references therein) and insight has developed over the last three decades.
By (L (X,Y )) we mean the set of linear bounded operators acting from the Hilbert space X to another Hilbert space Y. Fix some operator (Kin L(H_{5/2},H_{3/2} )).
A well-known parabolic problem with delay used in population dynamics is the so-called Hutchinson equation where B ( t ) is a time variable bounded nonlinear space operator acting on the delay term [8, 9].
ARFDEs where the operator acting on delay term is unbounded have been studied in some works.
Similar results are provided for F∞n⊗B K, K′) and W∞n⊗B K, K′), where B K, K′) is the set of all bounded linear operators acting on Hilbert spaces.
Let B ( H ) denote the C ∗ -algebra of all bounded linear operators acting on ℋ.
In this work we have studied the existence of almost periodic solutions of ARFDEs where the operator acting on the delay term is bounded.
Some applications and numerical methods for equations where the operator acting on the delay term is bounded have been studied in [5 8].
By defining a linear operator acting on the coefficient matrix of the filter, the optimality condition of the design problem is expressed as a linear operator equation.
Accordingly, a weak infinitesimal operator acting on the Lyapunov-Krasovskii functional is first proposed.
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