公共不變子空間與緊型條件（英）

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作　者：	曹鵬著
出版社：	科學(xué)出版社
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標(biāo)　簽：	暫缺

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ISBN：	9787030687128	出版時(shí)間：	2021-12-01	包裝：	平裝
開(kāi)本：	16開(kāi)	頁(yè)數(shù)：	196	字?jǐn)?shù)：

內(nèi)容簡(jiǎn)介

　　“Commoninvariantsubspacesandcompactnessconditions”一書(shū)主要總結(jié)了算子集合的不變子空間性質(zhì)，以及類(lèi)緊算元的相關(guān)結(jié)果。在算子理論中，我們把緊的擬冪零算子稱(chēng)為Volterra算子。由Volterra算子組成的集合亦稱(chēng)為Volterra集合，如Volterra半群，Volterra代數(shù)等。在《公共不變子空間與緊型條件》的第一部分，我們主要討論Volterra半群，Volterra李代數(shù)，Volterra約當(dāng)代數(shù)的不變子空間問(wèn)題，這些問(wèn)題都曾經(jīng)是算子理論、算子李代數(shù)中的經(jīng)典公開(kāi)問(wèn)題，在1999-2005年左右得以解決，收錄于《公共不變子空間與緊型條件》第一部分。在《公共不變子空間與緊型條件》的第二部分，我們討論了冪零李代數(shù)生成Banach代數(shù)是否為Engel代數(shù)的這一公開(kāi)問(wèn)題，這也是算子李代數(shù)的經(jīng)典問(wèn)題，至今尚未完全解決，相關(guān)部分結(jié)果收錄于第五章，隨后我們把緊算子的相關(guān)性質(zhì)向Banach代數(shù)中類(lèi)緊元集合推廣，給出了離散根的定義和性質(zhì)，*后，我們給出了離散根的擾動(dòng)理論，這從經(jīng)典的算子理論中的擾動(dòng)理論刻畫(huà)了離散根的本質(zhì)。除本人研究成果外，《公共不變子空間與緊型條件》亦收錄了著名算子理論學(xué)者Shulman，Turovskii，Kennedy等專(zhuān)家的從1999到2019年的相關(guān)成果。

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圖書(shū)目錄

Contents
Preface
Notation
Part I Preliminaries
Chapter 1 Banach Algebras 3
1.1 Jacobson radical and derivation 3
1.2 Analytic properties of the spectrum 5
1.3 Representation theory 6
Chapter 2 Operator Theory 8
2.1 Compact operators 8
2.2 Riesz and scattered operators 10
2.3 Decomposable operator 11
Chapter 3 Lie Algebras 15
3.1 Nilpotent and solvable Lie algebras 15
3.2 Engel algebras 17
3.3 Semisimple Lie algebras 20
Part II Beger-Wang Formulas and Applications
Chapter 4 Joint Spectral Radius 23
4.1 Preliminary properties 23
4.2 Joint quasinilpotence 26
4.3 Analytic properties 29
4.4 Hausdorff measure 31
4.5 Hausdorff and essential spectral radii 32
Chapter 5 Topological Radicals 36
5.1 Preliminary properties 36
5.2 Compactly quasinilpotent radical 37
5.3 Hypocompact radical 45
5.4 The radical rad ^ Rhc 50
Chapter 6 Beger-Wang Formula and Applications 52
6.1 Compactly quasinilpotence 52
6.2 Joint spectral radius on complete chain case 58
6.3 Beger-Wang formula 60
6.4 Coincidence of Hausdorff and essential radii 70
Chapter 7 Generalized Beger-Wang Formulas and Applications 75
7.1 Mixed GBWF 75
7.2 Operator GBWF 80
7.3 Banach algebraic GBWF 81
7.4 Volterra Lie algebra problem 83
Notes 90
Part III Volterra Ideal Theorem and Applications
Chapter 8 Elementary Spectral Manifolds 95
8.1 Preliminary properties 95
8.2 Algebraic and spatial formulas 99
8.3 Applications to scattered operators 103
Chapter 9 Volterra Ideal Problem 112
9.1 A reducibility criterion 112
9.2 Quasi-commutant and quasi-center 114
9.3 Solution of Volterra ideal problem 118
Chapter 10 Lie Algebras of Compact Operators 124
10.1 Engel and E-solvable ideals 124
10.2 ad-compact element 128
10.3 Largest E-solvable ideal 130
Chapter 11 Ad-Compact Lie Algebras 136
11.1 The largest Engel ideal 136
11.2 Irreducible representations by compact operators 138
11.3 E-solvable algebras and E-radical 141
Notes 149
Part IV Lie Algebras Generated by Special Operators
Chapter 12 Essentially Nilpotent Lie Algebras 153
12.1 Two Problems on operator Lie algebras 153
12.2 Nilpotent Lie algebras generated by decomposable operators 154
12.3 Lie algebras generated by quasinilpotent operators 156
12.4 Compact quasinilpotence 159
Chapter 13 Lie Algebras Generated by Operators on Hilbert Spaces 162
13.1 Finite dimensional selfadjoint Lie algebras 162
13.2 Finite dimensional semisimple Lie algebras 166
13.3 Selfadjoint ad-compact E-solvable Lie algebras 170
Chapter 14 Lie Algebras Generated by Jordan Operators 172
14.1 Lie algebras generated by normal operators 172
14.2 Lie algebras generated by Jordan operators 175
Chapter 15 Lie Algebras Generated by Riesz Operators 180
15.1 Engel Lie algebras 180
15.2 E-solvable Lie algebras 183
15.3 Applications to polynomially compact operators 189
Notes 191
Bibliography 192
Index 195