Modern Approaches to the Invariant-Subspace Problem

摘要: One of the major unsolved problems in operator theory is fifty-year-old invariant subspace problem, which asks whether every bounded linear on a Hilbert space has nontrivial closed subspace. This book presents some results area, including many that were derived within past few years and cannot be found other books. Beginning with preliminary chapter containing necessary pure mathematical background, authors present variety powerful techniques, use operator-valued Poisson kernel, various forms functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators moment sequences. The subject presented at level accessible to postgraduate students, as well established researchers. It will particular interest those who study also work areas mathematics.