scholarly journals Extreme points in spaces between Dirichlet and Vanishing Mean Oscillation

2003 ◽  
Vol 67 (3) ◽  
pp. 365-375
Author(s):  
K. J. Wirths ◽  
J. Xiao
Keyword(s):  
Unit Ball ◽  
Unit Circle ◽  
Dirichlet Space ◽  
Extreme Points ◽  
Closed Unit Ball ◽  
Mean Oscillation ◽  
Image Position ◽  
Complex Valued

For p ∈ (0, ∞) define Qp0(∂Δ) as the space of all Lebesgue measurable complex-valued functions f; on the unit circle ∂Δ for which ∫∂Δf;(z)|dz|/(2π) = 0 andas the open subarc I of ∂Δ varies. Note that each Qp,0(∂Δ) lies between the Dirichlet space and Sarason's vanishing mean oscillation space. This paper determines the extreme points of the closed unit ball of Qp,0(∂Δ) equipped with an appropriate norm.

Some Extreme Rays of the Positive Pluriharmonic Functions

1979 ◽  
Vol 31 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Frank Forelli
Keyword(s):  
Unit Ball ◽  
Extreme Point ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Compact Open Topology ◽  
Open Unit Ball ◽  
Pluriharmonic Functions ◽  
Image Position ◽  
Extreme Rays

1.1. We will denote by B the open unit ball in Cn, and we will denote by H(B) the class of all holomorphic functions on B. LetThus N(B) is convex (and compact in the compact open topology). We think that the structure of N(B) is of interest and importance. Thus we proved in [1] that if(1.1)if(1.2)and if n≧ 2, then g is an extreme point of N(B). We will denote by E(B) the class of all extreme points of N(B). If n = 1 and if (1.2) holds, then as is well known g ∈ E(B) if and only if(1.3)

scholarly journals Radial growth and exceptional sets for Cauchy–Stieltjes integrals

1994 ◽  
Vol 37 (1) ◽  
pp. 73-89 ◽  
Author(s):  
D. J. Hallenbeck ◽  
T. H. MacGregor
Keyword(s):  
Unit Circle ◽  
Radial Growth ◽  
Borel Measure ◽  
Local Conditions ◽  
Exceptional Sets ◽  
Image Position ◽  
Complex Valued

This paper considers the radial and nontangential growth of a function f given bywhere α>0 and μ is a complex-valued Borel measure on the unit circle. The main theorem shows how certain local conditions on μ near eiθ affect the growth of f(z) as z→eiθ in Stolz angles. This result leads to estimates on the nontangential growth of f where exceptional sets occur having zero β-capacity.

scholarly journals On Kadison's condition for extreme points of the unit ball in a B*-algebra

1969 ◽  
Vol 16 (3) ◽  
pp. 245-250 ◽  
Author(s):  
Bertram Yood
Keyword(s):  
Unit Ball ◽  
Banach Algebra ◽  
Extreme Points ◽  
Complex Banach Algebra ◽  
Image Position

Let B be a complex Banach algebra with an identity 1 and an involution x→x*. Kadison (1) has shown that, if B is a B*-algebra, [the set of extreme points of its unit ball coincides with the set of elements x of B for which

The Isometries of Hp

1964 ◽  
Vol 16 ◽  
pp. 721-728 ◽  
Author(s):  
Frank Forelli
Keyword(s):  
Unit Circle ◽  
Lebesgue Measure ◽  
Measurable Functions ◽  
Image Position ◽  
Complex Valued

Let a be the Lebesgue measure on the unit circle |z| = 1 withand let Lp be the space of complex-valued σ-measurable functions f such thatis finite. Hp is the closure in Lp of the algebra of analytic polynomials

A General form of the Functional LIL for Banach-Valued Brownian Motion

1984 ◽  
Vol 36 (6) ◽  
pp. 1046-1066
Author(s):  
H. Ship-Fah Wong
Keyword(s):  
Hilbert Space ◽  
Brownian Motion ◽  
Unit Ball ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Closed Unit Ball ◽  
General Version ◽  
Functional Lil ◽  
Image Position ◽  
Increasing Function

In a recent paper [12], C. Mueller proved a general version of the functional LIL which unifies Strassen's LIL and the Lévy modulus of continuity for Brownian motion W(t). His theorem also contains other known forms of the LIL.For each t ≧ 0, let be a family of points in the first quadrant of the plane. Let r ≦ 0; to each point (s0, l0), we associate a rectangleDefine Ar(t) to be the area of the union of these rectangles up to time t under the measure . Then, Theorem 1 [12, p. 166] states that for an increasing function h such thatthe set of limit points ofin C[0, 1] is the closed unit ball of the reproducing kernel Hilbert space (rkhs) associated with Wiener measure.

Geometry of balanced and absorbing subsets of topological modules

2019 ◽  
Vol 18 (06) ◽  
pp. 1950119 ◽  
Author(s):  
Francisco Javier García-Pacheco ◽  
Pablo Piniella
Keyword(s):  
Unit Ball ◽  
Extreme Points ◽  
Vector Spaces ◽  
Closed Unit Ball ◽  
Absorbing Set ◽  
Internal Point ◽  
Topological Vector Spaces ◽  
Topological Module ◽  
Real Algebra ◽  
Topological Modules

We define the concepts of balanced set and absorbing set in modules over topological rings, which coincide with the usual concepts when restricting to topological vector spaces. We show that in a topological module over an absolute semi-valued ring whose invertibles approach [Formula: see text], every neighborhood of [Formula: see text] is absorbing. We also introduce the concept of total closed unit neighborhood of zero (total closed unit) and prove that the only total closed unit of the quaternions [Formula: see text] is its closed unit ball [Formula: see text]. On the other hand, we also prove that if [Formula: see text] is an absolute semi-valued unital real algebra, then its closed unit ball [Formula: see text] is a total closed unit. Finally, we study the geometry of modules via the extreme points and the internal points, showing that no internal point can be an extreme point and that absorbance is equivalent to having [Formula: see text] as an internal point.

STRUCTURE TOPOLOGY AND EXTREME OPERATORS

2016 ◽  
Vol 95 (2) ◽  
pp. 315-321
Author(s):  
ANA M. CABRERA-SERRANO ◽  
JUAN F. MENA-JURADO
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Extreme Points ◽  
Closed Unit Ball ◽  
Structure Topology ◽  
Extreme Operator ◽  
Nice Operator

We say that a Banach space $X$ is ‘nice’ if every extreme operator from any Banach space into $X$ is a nice operator (that is, its adjoint preserves extreme points). We prove that if $X$ is a nice almost $CL$-space, then $X$ is isometrically isomorphic to $c_{0}(I)$ for some set $I$. We also show that if $X$ is a nice Banach space whose closed unit ball has the Krein–Milman property, then $X$ is $l_{\infty }^{n}$ for some $n\in \mathbb{N}$. The proof of our results relies on the structure topology.

Boundaries for polydisc algebras in infinite dimensions

1979 ◽  
Vol 85 (2) ◽  
pp. 291-303 ◽  
Author(s):  
J. Globevnik
Keyword(s):  
Unit Ball ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Open Unit ◽  
Closed Unit Ball ◽  
Infinite Dimensions ◽  
Open Unit Ball ◽  
Image Position ◽  
Bounded Continuous Functions ◽  
Uniformly Continuous

AbstractLet AB be the algebra of all bounded continuous functions on the closed unit ball B of c0, analytic on the open unit ball, with sup norm, and let AU be the sub-algebra of AB of those functions which are uniformly continuous on B. Call a set S ⊂ B a boundary of AB (AU) iffor every f ∈ AB (f ∈AU, respectively). In the paper we study the boundaries of AB and AU. We give a complete description of the boundaries of AU and present some necessary and some sufficient conditions for a set to be a boundary of AB. We also give some examples of boundaries.

Sign in / Sign up

Export Citation Format

Share Document