An introductory exposition of the study of operator theory, presenting an interesting and rapid approach to some results which are not normally treated in an introductory source. The volume includes recent results and coverage of the current state of the field.
Table of Contents
BOUNDED LINEAR OPERATORS ON A HILBERT SPACE. Linear and bilinear functionals. Inner product and norm. Hilbert spaces. Subspaces. Basis and dimension. Boundedness. Operators. STRUCTURE OF OPERATORS. Spectrum of operators. Spectral theorem for normal operators. Polar decomposition. The unitary part of contractions. The structure of isometries. The structure of quasinormal operators. The structure of subnormal operators with a cyclic vector. Invariant subspaces of subnormal operators. Hyponormal operators. Co-isometric extensions of contractions. BIBLIOGRAPHY.