EAN: 9783540415244

SIMILARITY PROBLEMS AND COMPLETELY BOUNDED MAPS...

These notes revolve around three similarity problems  appearing in three different contexts 
but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The
first one deals with group representations  the second one with C* -algebras and the third one
with the disc algebra. We describe them in detail in the introduction which follows. This
volume is devoted to the background necessary to understand these three problems  to the
solutions that are known in some special cases and to numerous related concepts  results 
counterexamples or extensions which their investigation has generated. While the three problems
seem different  it is possible to place them in a common framework using the key concept of
complete boundedness  which we present in detail. Using this notion  the three problems can all
be formulated as asking whether boundedness implies complete boundedness for linear maps
satisfying certain additional algebraic identities.

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