One of many significant unsolved difficulties in operator idea 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 publication offers many of the significant ends up in 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 history, the authors current various robust options, together with using the operator-valued Poisson kernel, quite a few kinds of the practical calculus, Hardy areas, fastened element theorems, minimum vectors, common operators and second sequences. the topic is gifted at a degree available to postgraduate scholars, in addition to validated researchers. it is going to be of specific curiosity to people who learn linear operators and in addition to people who paintings in different parts of natural arithmetic.
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