EXTREME POINTS AND SUPPORT POINTS OF A CLASS OF ANALYTIC FUNCTIONS

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)}).

Notes on Robinson's Sequential Lemma

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.

THE SUPPORT POINTS AND EXTREME POINTS OF THE UNIT BALL OF H'_P~ 1

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

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.

Topological Uniform Descent and Judgement of A-Weyl's Theorem

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.

Weakly Algebraic Ideal Topology of Effect Algebras

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.

Property (ω) for Operator Matrices

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.