主要总结了算子集合的不变子空间性质，以及类紧算元的相关结果。在算子理论中，我们把紧的拟幂零算子称为Volterra算子。由Volterra算子组成的集合亦称为Volterra集合，如Volterra半群，Volterra代数等。

Preface
Notation
Part Ⅰ Preliminaries
Chapter 1 Banach Algebras
1.1 Jaeobson radical and derivation
1.2 Analytic properties of the spectrum
1.3 Representation theory
Chapter 2 Operator Theory
2.1 Compact operators
2.2 Riesz and scattered operators
2.3 Decomposable operator
Chapter 3 Lie Algebras
3.1 Nilpotent and solvable Lie algebras
3.2 Engel algebras
3.3 Semisimple Lie algebras
Part Ⅱ Beger-Wang Formulas and Applications
Chapter 4 Joint Spectral Radius
4.1 Preliminary properties
4.2 Joint quasini]potence
4.3 Analytic properties
4.4 Hausdorff measure
4.5 Hausdorff and essential spectral radii
Chapter 5 Topological Radicals
5.1 Preliminary properties
5.2 Compactly quasinilpotent radical
5.3 Hypocompact radical
5.4 The radical rad A Rhc
Chapter 6 Beger-Wang Formula and Applications
6.1 Compactly quasinilpotence
6.2 Joint spectral radius on complete chain case
6.3 Beget-Wang formula
6.4 Coincidence of Hausdorff and essential radii
Chapter 7 Generalized Beger-Wang Formulas and Applications
7.1 Mixed GBWF
7.2 Operator GBWF
7.3 Banach algebraic GBWF
7.4 Volterra Lie algebra problem
Notes
Part Ⅲ Volterra Ideal Theorem and Applications
Chapter 8 Elementary Spectral Manifolds
8.1 Preliminary properties
8.2 Algebraic and spatial formulas
8.3 Applications to scattered operators
Chapter 9 Volterra Ideal Problem
9.1 A reducibility criterion
9.2 Quasi-commutant and quasi-center
9.3 Solution of Volterra ideal problem
Chapter I0 Lie Algebras of Compact Operators
10.1 Engel and E-solvable ideals
10.2 ad-compact element
10.3 Largest E-solvable ideal
Chapter 11 Ad-Compact Lie Algebras
11.1 The largest Engel ideal
11.2 Irreducible representations by compact operators
11.3 E-solvable algebras and E-radical
Notes
Part Ⅳ Lie Algebras Generated by Special Operators
Chapter 12 Essentially Nilpotent Lie Algebras
12.1 Two Problems on operator Lie algebras
12.2 Nilpotent Lie algebras generated by decomposable operators
12.3 Lie algebras generated by quasinilpotent operators
12.4 Compact quasinilpotence
Chapter 13 Lie Algebras Generated by Operators on Hflbert Spaces
13.1 Finite dimensional selfadjoint Lie algebras
13.2 Finite dimensional semisimple Lie algebras
13.3 Selfadjoint ad-compact E-solvable Lie algebras
Chapter 14 Lie Algebras Generated by Jordan Operators
14.1 Lie algebras generated by normal operators
14.2 Lie algebras generated by Jordan operators
Chapter 15 Lie Algebras Generated by Riesz Operators
15.1 Engel Lie algebras
15.2 E-solvable Lie algebras
15.3 Applications to polynomially compact operators
Notes
Bibliography
Index