This paper is devoted to the study of completely restricted Lie superalgebras. We give some sufficient and necessary conditions for both completely restricted Lie superalgebras and strongly completely restricted Lie s...This paper is devoted to the study of completely restricted Lie superalgebras. We give some sufficient and necessary conditions for both completely restricted Lie superalgebras and strongly completely restricted Lie superalgebras. Some other important results on completely restricted Lie superalgebras are also obtained.展开更多
This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X ...This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X the spectrum is disconnected unless it is a singleton. It shows that two strongly irreducible operators T1 and T2 on a ∑dc space are similar if and only if theK0-group of the commutant algebra of the direct sum T1 GT2 is isomorphic to the group of integers Z. On a ∑dc space X, it uses the semigroups of the commutant algebras of operators to give a condition that an operator is similar to some operator in （∑SI）（X）, it further gives a necessary and sufficient condition that two operators in （∑SI）（X） are similar by using the ordered K0-groups. It also proves that every operator in （∑SI）（X） has a unique （SI） decomposition up to similarity on a ∑dc space X, where （∑SI）（X） denotes the class of operators which can be written as a direct sum of finitely many strongly irreducible operators.展开更多
基金Youth Science Foundation of Northeast Normal University (111494027) National Natural Science Foundation of China (10271076)
文摘This paper is devoted to the study of completely restricted Lie superalgebras. We give some sufficient and necessary conditions for both completely restricted Lie superalgebras and strongly completely restricted Lie superalgebras. Some other important results on completely restricted Lie superalgebras are also obtained.
基金supported by National Natural Science Foundation of China (Grant No.11171066)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 2010350311001)+1 种基金Fujian Natural Science Foundation (Grant No. 2009J05002)Scientific Research Foundation of Fuzhou University (Grant No. 022459)
文摘This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X the spectrum is disconnected unless it is a singleton. It shows that two strongly irreducible operators T1 and T2 on a ∑dc space are similar if and only if theK0-group of the commutant algebra of the direct sum T1 GT2 is isomorphic to the group of integers Z. On a ∑dc space X, it uses the semigroups of the commutant algebras of operators to give a condition that an operator is similar to some operator in （∑SI）（X）, it further gives a necessary and sufficient condition that two operators in （∑SI）（X） are similar by using the ordered K0-groups. It also proves that every operator in （∑SI）（X） has a unique （SI） decomposition up to similarity on a ∑dc space X, where （∑SI）（X） denotes the class of operators which can be written as a direct sum of finitely many strongly irreducible operators.
