Classes of Linear Operators

ISBN-13: 9783034896795 / Angielski / Miękka / 2012 / 556 str.

Israel Gohberg; Seymour Goldberg; Marius A. Kaashoek

Opis

These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.

Spis treści

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.