Lyapunov theorems for operator algebras book

We generalize to such operator algebras several key theorems and concepts from the. For linear skewproduct threeparameter semiflows with discrete time acting on an arbitrary hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate lyapunov functions. Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This book presents the result of a systematic generalization of lyapunovs theorem to the setting of operator algebras. Lyapunov theorems for operator algebras ebook, 1991. Joel anderson in 1940 lyapunov proved that the range of a nonatomic vectorvalued measure is compact and convex. In 1940, a a lyapunov published his celebrated discovery that the range of a nonatomic vectorvalued measure is convex and compact. Akemann, joel anderson, lyapunov theorems for operator algebras english isbn. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations. This encompasses a number of classical results, such as lyapunov theorems.

This allows the reader to recognize the affinity between operator algebras and measure theory on locally compact spaces. In addition to the basic theorems of operator theory, including the spectral theorem, the geflandnaimark theorem, the double communtant theorem, and the kaplanski density theorem, some major topics covered by this text are. Akemann and explore their bibliography from s charles a. Lyapunov theorems for operator algebras books pics. Positive linear maps and the lyapunov equation springerlink. In the present memoir we take this theorem apart and perturb each hypothesis, thereby extending and. Lyapunov exponents of free operators sciencedirect. Advances and applications book series ot, volume abstract we show how general theorems on positive linear maps on matrices may be used in this context.