Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infini...Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).展开更多
The Infintesimal Prolongation Theorem is extended from sequences to nets in κ-saturated nonstandard model. As its application, a main property about the topology of uniform convergence is proved. The proof is much si...The Infintesimal Prolongation Theorem is extended from sequences to nets in κ-saturated nonstandard model. As its application, a main property about the topology of uniform convergence is proved. The proof is much simpler than it was; meanwhile, the nonstandard characteristics of convergence with respect to u.c. topology are given.展开更多
By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).
A Thomas type theorem is established for c0-and lp-multiplier convergence of a function series. This theorem contains some recent results as special cases.
In this paper,a-Browder’s theorem and a-Weyl’s theorem for bounded linear operators are studied by means of the property of the topological uniform descent.The sufficient and necessary conditions for a bounded linea...In this paper,a-Browder’s theorem and a-Weyl’s theorem for bounded linear operators are studied by means of the property of the topological uniform descent.The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding aBrowder’s theorem and a-Weyl’s theorem are established.As a consequence of the main result,the new judgements of a-Browder’s theorem and a-Weyl’s theorem for operator function are discussed.展开更多
In this paper, we show that every weakly a uniform topology (weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short) with which E is a first-countable, zero-dimensional, disconnect...In this paper, we show that every weakly a uniform topology (weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short) with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation + of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.展开更多
In this note,property (ω)and property 1 (ω)are variants of Weyl’s theorem. By means of topological uniform descent, the sufficient and necessary conditions of a bounded linear operator defined on a Hilbert spac...In this note,property (ω)and property 1 (ω)are variants of Weyl’s theorem. By means of topological uniform descent, the sufficient and necessary conditions of a bounded linear operator defined on a Hilbert space that satisfies property 1 (ω) and property (ω)is studied. Moreover, property 1 (ω)and property (ω)of 2 2operator matrices are discussed as well.展开更多
文摘Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).
基金Procject supported by the Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province, China
文摘The Infintesimal Prolongation Theorem is extended from sequences to nets in κ-saturated nonstandard model. As its application, a main property about the topology of uniform convergence is proved. The proof is much simpler than it was; meanwhile, the nonstandard characteristics of convergence with respect to u.c. topology are given.
文摘By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).
基金The Natrual Science Fund (A9621) of Heilongjiang Province.
文摘A Thomas type theorem is established for c0-and lp-multiplier convergence of a function series. This theorem contains some recent results as special cases.
基金Supported by the 2021 General Special Scientific Research Project of Education Department of Shaanxi Provincial Government(21JK0637)Science and Technology Planning Project of Weinan Science and Technology Bureau(2022ZDYFJH-11)2021 Talent Project of Weinan Normal University(2021RC16)。
文摘In this paper,a-Browder’s theorem and a-Weyl’s theorem for bounded linear operators are studied by means of the property of the topological uniform descent.The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding aBrowder’s theorem and a-Weyl’s theorem are established.As a consequence of the main result,the new judgements of a-Browder’s theorem and a-Weyl’s theorem for operator function are discussed.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401469 and 11171200)Shaanxi Province Natural Science Foundation(Grant No.2014JQ1032)
文摘In this paper, we show that every weakly a uniform topology (weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short) with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation + of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.
基金Supported by the Fundamental Research Funds for the Central Universities(GK200901015)Project for Outstanding Young and Middle-aged Researchers initiated by Tianshui Normal University(TSY201205)
文摘In this note,property (ω)and property 1 (ω)are variants of Weyl’s theorem. By means of topological uniform descent, the sufficient and necessary conditions of a bounded linear operator defined on a Hilbert space that satisfies property 1 (ω) and property (ω)is studied. Moreover, property 1 (ω)and property (ω)of 2 2operator matrices are discussed as well.