scholarly journals Properties of the Berezin transform of bounded functions

1999 ◽  
Vol 59 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Jaesung Lee
Keyword(s):  
Unit Circle ◽  
Convex Combination ◽  
Berezin Transform ◽  
Direct Sum ◽  
Bounded Functions

We find the spectrum of the Berezin operator T on L∞(Bn), then we show that if f ∈ L∞(Bn) satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of T, then f is M-harmonic.Finally we decompose the subspace of L∞(Bn) where lim Tkf exists into the direct sum of two subspaces of L∞(Bn).

Classification of Inductive Limits of Outer Actions of ℝ on Approximate Circle Algebras

2012 ◽  
Vol 55 (1) ◽  
pp. 73-80
Author(s):  
Andrew J. Dean
Keyword(s):  
Dynamical Systems ◽  
Unit Circle ◽  
Continuous Functions ◽  
Inductive Limits ◽  
Matrix Algebras ◽  
Direct Sum

AbstractIn this paper we present a classification, up to equivariant isomorphism, of C*-dynamical systems (A, ℝ, α) arising as inductive limits of directed systems ﹛(An, ℝ, αn), φnm﹜, where each An is a finite direct sum of matrix algebras over the continuous functions on the unit circle, and the αns are outer actions generated by rotation of the spectrum.

A VECTOR-VALUED VERSION OF RUSSO–DYE THEOREM

2009 ◽  
Vol 11 (06) ◽  
pp. 1035-1048
Author(s):  
J. C. NAVARRO-PASCUAL ◽  
M. G. SÁNCHEZ-LIROLA
Keyword(s):  
Unit Ball ◽  
Convex Combination ◽  
Extreme Points ◽  
Closed Convex Hull ◽  
Real Vector ◽  
Compact Metric Space ◽  
Bounded Functions ◽  
Vector Valued ◽  
Uniformly Continuous ◽  
Extremal Structure

In this paper, we will study the extremal structure of the unit ball of U(M,X), the space of uniformly continuous and bounded functions, from a not necessarily compact metric space M into a normed space X. Concretely, if X is uniformly convex and dim X ≥ 2, where dim X denotes the dimension of X as a real vector space, it is proved that every element y in U(M,X), with ‖y‖ < 1, is a convex combination of a finite number of extreme points of the unit ball. As a result, the unit ball of U(M,X) coincides with the closed-convex hull of its extreme points.

The Restricted Arc-Width of a Graph

10.37236/1734 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
David Arthur
Keyword(s):  
Unit Circle ◽  
Single Point ◽  
Minimum Width ◽  
Graph Operations ◽  
Function Mapping

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Barát and Hajnal on this subject and develop a generalization we call restricted arc-width. Our main results revolve around using this to bound arc-width from below and to examine the effect of several graph operations on arc-width. In particular, we completely describe the effect of disjoint unions and wedge sums while providing tight bounds on the effect of cones.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

scholarly journals Nonsingular bilinear forms on direct sums of ideals

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Beata Rothkegel
Keyword(s):  
Bilinear Form ◽  
Dedekind Domain ◽  
Bilinear Forms ◽  
Direct Sums ◽  
Direct Sum

AbstractIn the paper we formulate a criterion for the nonsingularity of a bilinear form on a direct sum of finitely many invertible ideals of a domain. We classify these forms up to isometry and, in the case of a Dedekind domain, up to similarity.

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