scholarly journals On a characterization of type I $C^ *$-algebras

1966 ◽  
Vol 72 (3) ◽  
pp. 508-513 ◽  
Author(s):  
Shôichirô Sakai
Keyword(s):  
Type I ◽  
C Algebras

scholarly journals AN INTERNAL CHARACTERIZATION OF COMPLETE POSITIVITY FOR ELEMENTARY OPERATORS

2002 ◽  
Vol 45 (2) ◽  
pp. 285-300
Author(s):  
Richard M. Timoney
Keyword(s):  
Linear Operators ◽  
Type I ◽  
Complete Positivity ◽  
Elementary Operator ◽  
Bounded Linear ◽  
C Algebra ◽  
C Algebras ◽  
Metric Operator ◽  
Elementary Operators

AbstractComplete positivity of ‘atomically extensible’ bounded linear operators between $C^*$-algebras is characterized in terms of positivity of a bilinear form on certain finite-rank operators. In the case of an elementary operator on a $C^*$-algebra, the approach leads us to characterize k-positivity of the operator in terms of positivity of a quadratic form on a subset of the dual space of the algebra and in terms of a certain inequality involving factorial states of finite type I.As an application we characterize those $C^*$-algebras where every k-positive elementary operator on the algebra is completely positive. They are either k-subhomogeneous or k-subhomogeneous by antiliminal. We also give a dual approach to the metric operator space introduced by Arveson.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 47B47; 47B65

scholarly journals Geometric Classification of Graph C*-algebras over Finite Graphs

2018 ◽  
Vol 70 (2) ◽  
pp. 294-353 ◽  
Author(s):  
Søren Eilers ◽  
Gunnar Restorff ◽  
Efren Ruiz ◽  
Adam P.W. Sørensen
Keyword(s):  
Standard Condition ◽  
Classification Problem ◽  
Complete Classification ◽  
Type I ◽  
Simple Graphs ◽  
Finite Graphs ◽  
C Algebras ◽  
Special Case

AbstractWe address the classification problem for graph C*-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that the graphs satisfy the standard condition (K), so that the graph C*-algebras may come with uncountably many ideals.We find that in this generality, stable isomorphism of graph C*-algebras does not coincide with the geometric notion of Cuntz move equivalence. However, adding a modest condition on the graphs, the two notions are proved to be mutually equivalent and equivalent to the C*-algebras having isomorphicK-theories. This proves in turn that under this condition, the graph C*-algebras are in fact classifiable byK-theory, providing, in particular, complete classification when the C* - algebras in question are either of real rank zero or type I/postliminal. The key ingredient in obtaining these results is a characterization of Cuntz move equivalence using the adjacency matrices of the graphs.Our results are applied to discuss the classification problem for the quantumlens spaces defined by Hong and Szymański, and to complete the classification of graph C*-algebras associated with all simple graphs with four vertices or less.

Characterization of type I-F CRISPR-Cas system in Laribacter hongkongensis isolates from animals, the environment and diarrhea patients

2021 ◽  
Vol 346 ◽  
pp. 109153
Author(s):  
Ling Wang ◽  
Li Wang ◽  
Youzhao Liu ◽  
Zhiyun Wang ◽  
Qing Chen ◽  
...  
Keyword(s):  
Type I ◽  
Laribacter Hongkongensis

scholarly journals Molecular and Pharmacological Characterization of the Interaction between Human Geranylgeranyltransferase Type I and Ras-Related Protein Rap1B

2021 ◽  
Vol 22 (5) ◽  
pp. 2501
Author(s):  
Sonja Hinz ◽  
Dominik Jung ◽  
Dorota Hauert ◽  
Hagen S. Bachmann
Keyword(s):  
Protein Function ◽  
Tumor Development ◽  
Cysteine Residue ◽  
Type I ◽  
Pharmacological Characterization ◽  
Anti Cancer ◽  
And Function ◽  
Caax Motif ◽  
Important Drug

Geranylgeranyltransferase type-I (GGTase-I) represents an important drug target since it contributes to the function of many proteins that are involved in tumor development and metastasis. This led to the development of GGTase-I inhibitors as anti-cancer drugs blocking the protein function and membrane association of e.g., Rap subfamilies that are involved in cell differentiation and cell growth. In the present study, we developed a new NanoBiT assay to monitor the interaction of human GGTase-I and its substrate Rap1B. Different Rap1B prenylation-deficient mutants (C181G, C181S, and ΔCQLL) were designed and investigated for their interaction with GGTase-I. While the Rap1B mutants C181G and C181S still exhibited interaction with human GGTase-I, mutant ΔCQLL, lacking the entire CAAX motif (defined by a cysteine residue, two aliphatic residues, and the C-terminal residue), showed reduced interaction. Moreover, a specific, peptidomimetic and competitive CAAX inhibitor was able to block the interaction of Rap1B with GGTase-I. Furthermore, activation of both Gαs-coupled human adenosine receptors, A2A (A2AAR) and A2B (A2BAR), increased the interaction between GGTase-I and Rap1B, probably representing a way to modulate prenylation and function of Rap1B. Thus, A2AAR and A2BAR antagonists might be promising candidates for therapeutic intervention for different types of cancer that overexpress Rap1B. Finally, the NanoBiT assay provides a tool to investigate the pharmacology of GGTase-I inhibitors.

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