By Professor Isabelle Chalendar, Jonathan R. Partington
One of many significant unsolved difficulties in operator conception is the fifty-year-old invariant subspace challenge, which asks even if each bounded linear operator on a Hilbert area has a nontrivial closed invariant subspace. This ebook offers the various significant leads to the world, together with many who have been derived in the earlier few years and can't be present in different books. starting with a initial bankruptcy containing the required natural mathematical heritage, the authors current a number of robust innovations, together with using the operator-valued Poisson kernel, quite a few varieties of the sensible calculus, Hardy areas, mounted element theorems, minimum vectors, common operators and second sequences. the topic is gifted at a degree obtainable to postgraduate scholars, in addition to proven researchers. it will likely be of specific curiosity to those that learn linear operators and in addition to people who paintings in different parts of natural arithmetic.