Download E-books Similarity Problems and Completely Bounded Maps (Lecture Notes in Mathematics) PDF

By Gilles Pisier

Those notes revolve round 3 similarity difficulties, showing in 3 various contexts, yet all facing the gap B(H) of all bounded operators on a posh Hilbert area H. the 1st one offers with team representations, the second with C* -algebras and the 3rd one with the disc algebra. We describe them intimately within the creation which follows. This quantity is dedicated to the history essential to comprehend those 3 difficulties, to the strategies which are identified in a few exact circumstances and to varied comparable ideas, effects, counterexamples or extensions which their research has generated. whereas the 3 difficulties look diverse, it truly is attainable to put them in a typical framework utilizing the main thought of "complete boundedness", which we found in element. utilizing this concept, the 3 difficulties can all be formulated as asking even if "boundedness" implies "complete boundedness" for linear maps fulfilling sure extra algebraic identities.

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