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Full-Text Articles in Physical Sciences and Mathematics
Norming Algebras And Automatic Complete Boundedness Of Isomorphisms Of Operator Algebras, David R. Pitts
Norming Algebras And Automatic Complete Boundedness Of Isomorphisms Of Operator Algebras, David R. Pitts
Department of Mathematics: Faculty Publications
We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C*-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomorphism of a C*-algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a C-algebra is similar to a -representation precisely when the image operator algebra -norms itself. We give …
Robustness With Respect To Sampling For Stabilization Of Riesz Spectral Systems, Richard Rebarber, Stuart Townley
Robustness With Respect To Sampling For Stabilization Of Riesz Spectral Systems, Richard Rebarber, Stuart Townley
Department of Mathematics: Faculty Publications
We suppose that a continuous-time feedback is input–output stabilizing for an infinite-dimensional system. We address the question of whether the sampled-data controller obtained by applying idealized sample-and-hold to this continuous-time feedback is also input–output stabilizing if the sampling time is small enough. This question has been previously addressed for fairly general systems under various conditions. In this note, we restrict our attention to Riesz spectral systems, for which we generalize the existing results. Specifically, we give two relatively simple conditions which, combined, are sufficient for the sampled-data controller to be stabilizing. The first condition is a spectrum decomposition for the …
Asymptotic Stability Of A Fluid-Structure Semigroup, George Avalos
Asymptotic Stability Of A Fluid-Structure Semigroup, George Avalos
Department of Mathematics: Faculty Publications
The strong stability problem for a fluid-structure interactive partial differential equation (PDE) is considered. The PDE comprises a coupling of the linearized Stokes equations to the classical system of elasticity, with the coupling occurring on the boundary interface between the fluid and solid media. It is now known that this PDE may be modeled by a $C_{0}$-semigroup of contractions on an appropriate Hilbert space. However, because of the nature of the unbounded coupling between fluid and structure, the resolvent of the semigroup generator will \emph{not} be a compact operator. In consequence, the classical solution to the stability problem, by means …