Operator Algebras of Functions

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar multipliers of a vector-valued reproducing kernel Hilbert space. We use these to further develop a quantized function theory for various domains that extends and unifies Agler's theory of commuting contractions and the Arveson-Drury-Popescu theory of commuting row contractions. We obtain analogous factorization theorems, prove that the algebras that we obtain are dual operator algebras and show that for many domains, supremums over all commuting tuples of operators satisfying certain inequalities are obtained over all commuting tuples of matrices.Comment: 33 page

CcpC-dependent regulation of citrate synthase gene expression in Listeria monocytogenes

Citrate synthase, the first and rate-limiting enzyme of the tricarboxylic acid branch of the Krebs cycle, was shown to be required for de novo synthesis of glutamate and glutamine in Listeria monocytogenes. The citrate synthase (citZ) gene was found to be part of a complex operon with the upstream genes lmo 1569 and lmo 1568. The downstream isocitrate dehydrogenase (citC) gene appears to be part of the same operon as well. Two promoters were shown to drive citZ expression, a distal promoter located upstream of lmo 1569 and a proximal promoter located upstream of the lmo 1568 gene. Transcription of citZ from both promoters was regulated by CcpC by interaction with a single site; assays of transcription in vivo and assays of CcpC binding in vitro revealed that CcpC interacts with and represses the proximal promoter that drives expression of the lmo 1568, citZ, and citC genes and, by binding to the same site, prevents read-through transcription from the distal, lmo 1569 promoter. Expression of the lmo 1568 operon was not affected by the carbon source but was repressed during growth in complex medium by addition of glutamine.Public Health Service GM03671

CcpC-Dependent Regulation of Citrate Synthase Gene Expression in Listeria monocytogenes▿

Citrate synthase, the first and rate-limiting enzyme of the tricarboxylic acid branch of the Krebs cycle, was shown to be required for de novo synthesis of glutamate and glutamine in Listeria monocytogenes. The citrate synthase (citZ) gene was found to be part of a complex operon with the upstream genes lmo1569 and lmo1568. The downstream isocitrate dehydrogenase (citC) gene appears to be part of the same operon as well. Two promoters were shown to drive citZ expression, a distal promoter located upstream of lmo1569 and a proximal promoter located upstream of the lmo1568 gene. Transcription of citZ from both promoters was regulated by CcpC by interaction with a single site; assays of transcription in vivo and assays of CcpC binding in vitro revealed that CcpC interacts with and represses the proximal promoter that drives expression of the lmo1568, citZ, and citC genes and, by binding to the same site, prevents read-through transcription from the distal, lmo1569 promoter. Expression of the lmo1568 operon was not affected by the carbon source but was repressed during growth in complex medium by addition of glutamine