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Banach Algebra Techniques in Operator Theory
The study of interrelationships between rectifiable currents associated to n-tuples of operators with commutators or multicommutators satisfying trace class conditions is the exploration of a non commutative spectral theory in which there is still a significant degree of localization at points in the current support - viewed as a non commutative spectrum. This memoir is a systematic development of the theory of principal functions in this the noncommutative case, and it generalizes extensive previous work of R. Carey and Pincus.
A discussion of certain advanced topics in operator theory, providing the necessary background while assuming only standard senior-first year graduate courses in general topology, measure theory, and algebra. Each chapter ends with source notes which suggest additional reading along with comments on who proved what and when, followed by a large number of problems of varying difficulty. This new edition will appeal to a whole new generation of students seeking an introduction to this topic.