In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.
In this article, the author introduces the generalized difference paranormed sequence spaces c （△v^m, f, p, q, s）, c0 （△v^m, f, p, q, s）, and l∞ （△v^m, f, p, q, s） defined over a seminormed sequence space （...In this article, the author introduces the generalized difference paranormed sequence spaces c （△v^m, f, p, q, s）, c0 （△v^m, f, p, q, s）, and l∞ （△v^m, f, p, q, s） defined over a seminormed sequence space （X, q）. The author also studies their properties like completeness, solidity, symmetricitv, etc.展开更多
Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_...Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_i = 1,x_i ∈ C^n},where Cn is an n-dimensional vector space over complex field C.In this paper we studynorm properties and stability of y-numerical radius.展开更多
We give a functional representation theorem for a class of real p-Banach algebras. This theorem is used to show that every p-homogeneous seminorm with square property on a real associative algebra is
In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.
A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra t...A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is necessarily Lipschitz. We come to the result that the free product of two unital completely Lipschitz contractive *-homomorphisms from upper related C*-metric algebras coming from *-filtrations to those which are lower related is a unital Lipschitz *-homomorphism.展开更多
Let I 2N be an ideal and let XI = span{χI ： I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to p...Let I 2N be an ideal and let XI = span{χI ： I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to pI-kernel convergence. In addition, let K = {x＊oχ（·） ： x＊∈ p（e）}, where p（x） = lim supn→∞1/n（∑k=1n｜x（k）｜, and let Iμ = {A N ： μ（A） = 0} for all μ = x＊oχ（·） ∈ K. Then Iμ is a proper ideal. We also show that the ideal convergence deduced by the proper ideal Iμ, the p-kernel convergence and the statistical convergence are also equivalent.展开更多
In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble gro...In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.展开更多
文摘In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.
文摘In this article, the author introduces the generalized difference paranormed sequence spaces c （△v^m, f, p, q, s）, c0 （△v^m, f, p, q, s）, and l∞ （△v^m, f, p, q, s） defined over a seminormed sequence space （X, q）. The author also studies their properties like completeness, solidity, symmetricitv, etc.
基金Supported by the Natural Science Foundation of Hubei Province（2004X157）
文摘Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_i = 1,x_i ∈ C^n},where Cn is an n-dimensional vector space over complex field C.In this paper we studynorm properties and stability of y-numerical radius.
文摘We give a functional representation theorem for a class of real p-Banach algebras. This theorem is used to show that every p-homogeneous seminorm with square property on a real associative algebra is
文摘In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.
基金supported by the Shanghai Leading Academic Discipline Project (Project No. B407)National Natural Science Foundation of China (Grant No. 10671068)
文摘A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is necessarily Lipschitz. We come to the result that the free product of two unital completely Lipschitz contractive *-homomorphisms from upper related C*-metric algebras coming from *-filtrations to those which are lower related is a unital Lipschitz *-homomorphism.
基金supported by Plan Project of Education Department of Fujian Province(Grant No.JA11275)
文摘Let I 2N be an ideal and let XI = span{χI ： I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to pI-kernel convergence. In addition, let K = {x＊oχ（·） ： x＊∈ p（e）}, where p（x） = lim supn→∞1/n（∑k=1n｜x（k）｜, and let Iμ = {A N ： μ（A） = 0} for all μ = x＊oχ（·） ∈ K. Then Iμ is a proper ideal. We also show that the ideal convergence deduced by the proper ideal Iμ, the p-kernel convergence and the statistical convergence are also equivalent.
文摘In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.
