Abstract
I. General Theory. Operators on Finite-Dimensional Spaces. Elementary Spectral Theory. The Orbits of a Linear Operator. II. Compactness and its Applications. Spectral Theory for Compact Operators. Topologies on the Space of Operators. III. Banach Algebras Techniques. Banach Algebras. Normal Operators. IV. Analytic Functions. Banach Spaces of Analytic Functions. The Multiplication by e itheta on H 2 (Pi) and L 2 (Pi). V. Dilations and Extensions. Minimal Dilation of a Contraction. The H # Functional Calculus. C 1 -Contractions. VI. Invariant Subspaces. Positive Results. A Counter-Example to the Invariant Subspace Problem. Exercises. Index. References.
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