scholarly journals Characterizations of tripotents in JB*-triples

2006 ◽  
Vol 99 (1) ◽  
pp. 147 ◽  
Author(s):  
Remo V. Hügli
Keyword(s):  
Unit Ball ◽  
Partial Order ◽  
Facial Structure ◽  
Partial Isometries ◽  
C Algebras ◽  
Metric Characterization

The set $\mathcal{U}(A)$ of tripotents in a $\mathrm{JB}^*$-triple $A$ is characterized in various ways. Some of the characterizations use only the norm-structure of $A$. The partial order on $\mathcal{U}(A)$ as well as $\sigma$-finiteness of tripotents are described intrinsically in terms of the facial structure of the unit ball $A_1$ in $A$, i.e. without reference to the (pre-)dual of $A$. This extends similar results obtained in [6] and simplifies the metric characterization of partial isometries in $C^*$-algebras found in [1](cf. [8].

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

scholarly journals CUNTZ–PIMSNER C*-ALGEBRAS ASSOCIATED WITH SUBSHIFTS

2008 ◽  
Vol 19 (01) ◽  
pp. 47-70 ◽  
Author(s):  
TOKE MEIER CARLSEN
Keyword(s):  
Partial Isometries ◽  
C Algebra ◽  
C Algebras ◽  
Shift Space

By using C*-correspondences and Cuntz–Pimsner algebras, we associate to every subshift (also called a shift space) 𝖷 a C*-algebra [Formula: see text], which is a generalization of the Cuntz–Krieger algebras. We show that [Formula: see text] is the universal C*-algebra generated by partial isometries satisfying relations given by 𝖷. We also show that [Formula: see text] is a one-sided conjugacy invariant of 𝖷.

A Characterization of Bergman Spaces on the Unit Ball of ℂn. II

2012 ◽  
Vol 55 (1) ◽  
pp. 146-152 ◽  
Author(s):  
Songxiao Li ◽  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Double Integrals

AbstractIt has been shown that a holomorphic function f in the unit ball of ℂn belongs to the weighted Bergman space , p > n + 1 + α, if and only if the function | f(z) – f(w)|/|1 – 〈z, w〉| is in Lp( × , dvβ × dvβ), where β = (p + α – n – 1)/2 and dvβ(z) = (1 – |z|2)βdv(z). In this paper we consider the range 0 < p < n + 1 + α and show that in this case, f ∈ (i) if and only if the function | f(z) – f(w)|/|1 – hz, wi| is in Lp( × , dvα × dvα), (ii) if and only if the function | f(z)– f(w)|/|z–w| is in Lp( × , dvα × dvα). We think the revealed difference in the weights for the double integrals between the cases 0 < p < n + 1 + α and p > n + 1 + α is particularly interesting.

scholarly journals A CHARACTERIZATION OF WEIGHTED BERGMAN-PRIVALOV SPACES ON THE UNIT BALL OF Cn

2002 ◽  
Vol 39 (5) ◽  
pp. 783-800 ◽  
Author(s):  
Yasuo Matsugu ◽  
Jun Miyazawa ◽  
Sei-Ichiro Ueki
Keyword(s):  
Unit Ball

scholarly journals A characterization of semiprojectivity for commutative C *-algebras

2012 ◽  
Vol 105 (5) ◽  
pp. 1021-1046 ◽  
Author(s):  
Adam P. W. Sørensen ◽  
Hannes Thiel
Keyword(s):  
C Algebras

Partial isometries and an invariant of C*-algebras

2011 ◽  
Vol 27 (4) ◽  
pp. 799-806 ◽  
Author(s):  
Hong Liang Yao ◽  
Xiao Chun Fang
Keyword(s):  
Partial Isometries ◽  
C Algebras

On partial isometries in C*-algebras

2011 ◽  
Vol 205 (1) ◽  
pp. 71-82 ◽  
Author(s):  
M. Laura Arias ◽  
Mostafa Mbekhta
Keyword(s):  
Partial Isometries ◽  
C Algebras

scholarly journals Complex extreme measurable selections

1995 ◽  
Vol 58 (2) ◽  
pp. 222-231
Author(s):  
Douglas Mupasiri
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Extreme Point ◽  
Measure Space ◽  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Closed Unit Ball ◽  
Measurable Selections ◽  
Necessary And Sufficient

AbstractWe give a characterization of complex extreme measurable selections for a suitable set-valued map. We use this result to obtain necessary and sufficient conditions for a function to be a complex extreme point of the closed unit ball of Lp (ω, Σ, ν X), where (ω, σ, ν) is any positive, complete measure space, X is a separable complex Banach space, and 0 < p < ∞.

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