V: Triangular Representations.- XX. Additive lower-upper triangular decompositions of operators.- XXI. Operators in triangular form.- XXII. Multiplicative lower-upper triangular decompositions of operators.- VI: Classes of Toeplitz Operators.- XXIII. Block Toeplitz operators.- XXIV. Toeplitz operators defined by rational matrix functions.- XXV. Toeplitz operators defined by piecewise continuous matrix functions.- VII: Contractive Operators and Characteristic Operator Functions.- XXVI. Block shift operators.- XXVII. Dilation theory.- XXVIII. Unitary systems and characteristic operator functions.- VIII: Banach Algebras And Algebras Of Operators.- XXIX. General theory.- XXX. Commutative Banach algebras.- XXXI. Elements of C*-algebra theory.- XXXII. Banach algebras generated by Toeplitz operators.- IX: Extension and Completion Problems.- XXXIII. Completions of matrices.- XXXIV. A general scheme for completion and extension problems.- XXXV. Applications of the band method.- Standard references texts.- List of symbols.

Rese�a del editor

This - book offers a panoptic view of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. This second volume consists of five parts: triangular representations, classes of Toeplitz operators, contractive operators and characteristic operator functions, Banach algebras and algebras of operators, and extension and completion problems. The exposition is self-contained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering.

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