SIMILARITY PROBLEMS

摘要

We present the solution to a question raised by Halmos (1970): for any ε > 0 there is an operator T in B(H) such thatrn(1) (A)P polynomial ||P(T)|| ≤ (| +ε)||P||_∞rn(where ||P||_∞ = sup z ∈D |P(z)|) but which is not similar to a contraction.rnWe will outline the construction which combines ideas from Operator Space Theory (namely Paulsen's criterion for similarity to a contraction) and ideas from the theory of Hanhel operators (namely a kind of example proposed by Peller).