Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrice...Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.展开更多
In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be in...In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be infinite dimensional Banach spaces over complex field A. Denote by Y} the set of all bounded linear operators from X to Y. If X=Y, we write instead of B(X, F). For T^B(X"), let -D(T), ker T, R(T} denote the domain, kerner and the range of T respectively. For a subset MdX, M denotes the closure of M. Let H be a Hilbert space and MdH, then ML denotes the annihilator of If.展开更多
Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n×n matrix A over R is expressible as a sum A=E1+…+Es+N of(commuting)idempotent matrices Ei and a nilpo...Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n×n matrix A over R is expressible as a sum A=E1+…+Es+N of(commuting)idempotent matrices Ei and a nilpotent matrix N.展开更多
We classify all polynomial maps of the form H=(u(x,y,z),v(x,y,z),h(x,y))in the case when the Jacobian matrix of H is nilpotent and the highest degree of z in v is no more than 1.In addition,we generalize the structure...We classify all polynomial maps of the form H=(u(x,y,z),v(x,y,z),h(x,y))in the case when the Jacobian matrix of H is nilpotent and the highest degree of z in v is no more than 1.In addition,we generalize the structure of polynomial maps H to H=(H_(1)(x_(1),x_(2),…,x_(n)),b_(3)x_(3)+…+b_(n)x_(n)+H^((0))_(2)(x_(2)),H_(3)(x_(1),x_(2)),…,H_(n)(x_(1),x_(2))).展开更多
文摘Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.
文摘In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be infinite dimensional Banach spaces over complex field A. Denote by Y} the set of all bounded linear operators from X to Y. If X=Y, we write instead of B(X, F). For T^B(X"), let -D(T), ker T, R(T} denote the domain, kerner and the range of T respectively. For a subset MdX, M denotes the closure of M. Let H be a Hilbert space and MdH, then ML denotes the annihilator of If.
基金supported by Ministry of Educations,Science and Technological Development of Republic of Serbia Project#174032.
文摘Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n×n matrix A over R is expressible as a sum A=E1+…+Es+N of(commuting)idempotent matrices Ei and a nilpotent matrix N.
基金Supported by the National Natural Science Foundation of China(Grant No.11601146,11871241)the Natural Science Foundation of Hunan Province(Grant No.2016JJ3085)the Construct Program of the Key Discipline in Hunan Province.
文摘We classify all polynomial maps of the form H=(u(x,y,z),v(x,y,z),h(x,y))in the case when the Jacobian matrix of H is nilpotent and the highest degree of z in v is no more than 1.In addition,we generalize the structure of polynomial maps H to H=(H_(1)(x_(1),x_(2),…,x_(n)),b_(3)x_(3)+…+b_(n)x_(n)+H^((0))_(2)(x_(2)),H_(3)(x_(1),x_(2)),…,H_(n)(x_(1),x_(2))).