Hilbert Space Operators: A Problem Solving ApproachThis self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines. |
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according to Problem Banach space compact operator completely nonunitary complex Banach space complex Hilbert space converges decomposition diagonal dimension greater direct summand exists a nonscalar finite finite-dimensional following assertions hence hyponormal operators implies inner product space integer invariant subspace problem invertible isometry lies linear manifold linear transformation Lomonosov Theorem Math Moreover nilpotent nonnegative operators nonscalar operator nontrivial hyperinvariant subspace nontrivial invariant subspace nonzero compact operator nonzero vector normaloid normed space null oc(T op(T operator that commutes Operator Theory orthogonal projection paranormal operator polynomial proof proper contraction prove the following quasihyponormal quasinormal operator Recall scalar self-adjoint operators self-commutator semi-quasihyponormal shift of multiplicity Show Solution space H space of dimension strongly stable subnormal operators subset Suppose T-invariant T*Tx Take an arbitrary trivially unilateral shift unilateral weighted shift unitarily equivalent unitary weakly stable