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目次

I Preliminaries.- A Lie Algebras.- § 1 Basic facts.- § 2 Ideals, solvability, nilpotence, radical and semisimplicity.- § 3 SP classes of solvable Lie algebras.- § 4 Radical splitting theorems.- § 5 Cartan subalgebras.- § 6 The Killing form and compact Lie algebras.- § 7 Lie *-algebras.- B Complexes.- § 8 Generalities.- § 9 Banach space complexes.- § 10 Koszul complexes.- § 11 Operations with the Koszul complexes: duality and tensor products.- C Spectral Theory in Complex Banach Space.- § 12 General spectral theory and decomposable operators.- § 13 The transformation of the spectral maximal subspaces by bounded operators.- § 14 Special classes of decomposable operators.- Notes.- II The Commutators and Nilpotence Criteria.- § 15 An asymptotic formula for the commutators.- § 16 Nilpotence criteria in an associative algebra.- § 17 Quasinilpotence and nilpotence criteria in complex Banach algebras.- § 18 Nilpotent elements in LM-decomposable Lie subalgebras of an associative algebra.- § 19 Nilpotent elements in LM-decomposable Lie algebras of bounded linear operators.- Notes.- III Infinite-dimensional Variants of the Lie and Engel Theorems.- § 20 Weights for operator algebras.- § 21 Invariant subspaces for LM-decomposable Lie algebras of bounded operators.- § 22 The irreducible representations of an LM-decomposable Lie algebra. Infinite-dimensional variant of Lie's Theorem on a complex Banach space.- § 23 The associative envelope of a Lie algebra of quasinilpotent operators.- § 24 Commutativity modulo the Jacobson radical.- Notes.- IV Spectral Theory for Solvable Lie Algebras of Operators.- § 25 Spectral theory for representations of Lie algebras.- § 26 Spectral theory for systems of operators generating nilpotent Lie algebras.- § 27 The Cartan-Taylor spectrum of a locally solvable Lie algebra of operators.- § 28 Lie ideals of generalized spectral operators.- Notes.- V Semisimple Lie Algebras of Operators.- § 29 Lie subalgebra with involution consisting of bounded operators on a complex Banach space. Normal elements given by a space of self-adjoint operators.- § 30 Individual spectral properties in ideally finite semisimple Lie algebras of operators.- § 31 Semisimple Lie algebras of compact quasinilpotent operators.- Notes.- List of Symbols.