By Bernard Beauzamy
This monograph purely calls for of the reader a easy wisdom of classical research: degree idea, analytic services, Hilbert areas, practical research. The ebook is self-contained, aside from a couple of technical instruments, for which unique references are given. half I begins with finite-dimensional areas and common spectral thought. yet very quickly (Chapter III), new fabric is gifted, resulting in new instructions for learn. Open questions are pointed out the following. half II matters compactness and its functions, not just spectral conception for compact operators (Invariant Subspaces and Lomonossov's Theorem) but in addition duality among the gap of nuclear operators and the distance of all operators on a Hilbert area, a end result that's seldom offered. half III includes Algebra strategies: Gelfand's conception, and alertness to general Operators. the following back, instructions for learn are indicated. half IV offers with analytic features, and features a few new advancements. A simplified, operator-oriented, model is gifted. half V offers dilations and extensions: Nagy-Foias dilation thought, and the author's paintings approximately C1-contractions. half VI offers with the Invariant Subspace challenge, with confident effects and counter-examples. usually, a lot new fabric is gifted. at the Invariant Subspace challenge, the extent of analysis is reached, either within the optimistic and unfavorable instructions.