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1.
A Note on Positivity of Elementary Operators   总被引:1,自引:0,他引:1  
We show that operators on n x n matrices which are representablein the form (where ai andbi are n x n matrices) and are k-positive for must be completely positive. As a consequence, elementaryoperators on a C*-algebra with minimal length l which are k-positivefor must be completely positive. 1991 Mathematics Subject Classification 47B47, 46L05, 47B65.  相似文献   
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We establish lower bounds for norms and CB-norms of elementary operators on . Our main result concerns the operator Ta,bx=axb+bxa and we show ‖Ta,b‖?‖a‖‖b‖, proving a conjecture of M. Mathieu. We also establish some other results and formulae for ‖Ta,bcb and ‖Ta,b‖ for special cases.  相似文献   
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BACKGROUND: Polyketides are structurally diverse natural products that have a range of medically useful activities. Nonaromatic bacterial polyketides are synthesised on modular polyketide synthase (PKS) multienzymes, in which each cycle of chain extension requires a different 'module' of enzymatic activities. Attempts to design and construct modular PKSs that synthesise specified novel polyketides provide a particularly stringent test of our understanding of PKS structure and function. RESULTS: We have constructed bimodular and trimodular PKSs based on DEBS1-TE, a derivative of the erythromycin PKS that contains only modules 1 and 2 and a thioesterase (TE), by substituting multiple domains with appropriate counterparts derived from the rapamycin PKS. Hybrid PKSs were obtained that synthesised the predicted target triketide lactones, which are simple analogues of cholesterol-lowering statins. In constructing intermodular fusions, whether between modules in the same or in different proteins, it was found advantageous to preserve intact the acyl carrier protein-ketosynthase (ACP-KS) didomain that spans the junction between successive modules. CONCLUSIONS: Relatively simple considerations govern the construction of functional hybrid PKSs. Fusion sites should be chosen either in the surface-accessible linker regions between enzymatic domains, as previously revealed, or just inside the conserved margins of domains. The interaction of an ACP domain with the adjacent KS domain, whether on the same polyketide or not, is of particular importance, both through conservation of appropriate protein-protein interactions, and through optimising molecular recognition of the altered polyketide chain in the key transfer of the acyl chain from the ACP of one module to the KS of the downstream module.  相似文献   
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Background: Modular polyketide synthases (PKSs) catalyse the biosynthesis of complex polyketides using a different set of enzymes for each successive cycle of chain extension. Directed biosynthesis starting from synthetic diketides is a potentially valuable route to novel polyketides. We have used a purified bimodular derivative of the erythromycin-producing polyketide synthase (DEBS 1-TE) to study chain extension starting from a variety of diketide analogues and, in some cases, from the alternative acyl-CoA thioester substrates.Results: Chain initiation in vitro by DEBS 1-TE module 2 using a synthetic diketide analogue as a substrate was tolerant of significant structural variation in the starter unit of the synthetic diketide, but other changes completely abolished activity. Interestingly, a racemic β-keto diketide was found to be reduced in situ on the PKS and utilised in place of its more complex hydroxy analogue as a substrate for chain extension. The presence of a diketide analogue strongly inhibited chain initiation via the loading module. Significantly higher concentrations of diketide N-acetylcysteamine analogues than their corresponding acyl-CoA thioesters are required to achieve comparable yields of triketide lactones.Conclusions: Although a broad range of variation in the starter residue is acceptable, the substrate specificity of module 2 of a typical modular PKS in vitro is relatively intolerant of changes at C-2 and C-3. This will restrict the usefulness of approaches to synthesise novel erythromycins using synthetic diketides in vivo. The use of synthetic β-keto diketides in vivo deserves to be explored.  相似文献   
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Every bounded domain in a complex Banach spaceE is biholomorphically equivalent to a finite product of irreducibles if and only ifE does not containc 0. A quantitative version of this holds if and only ifE has finite cotype.  相似文献   
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It is well-known that if T is a Dm-Dn bimodule map on the m × n complex matrices, then T is a Schur multiplier and 6T6cb=6T6. If n = 2 and T is merely assumed to be a right D2-module map, then we show that 6T6cb=6T6. However, this property fails if m ? 2 and n ? 3. For m ? 2 and n = 3, 4 or n ? m2 we give examples of maps T attaining the supremumC(m,n)=supT6cb:Ta rightDn-module map onMm,nwith6T61},we show that C(m,m2)=m and succeed in finding sharp results for C(m, n) in certain other cases. As a consequence, if H is an infinite-dimensional Hilbert space and D is a masa in B(H), then there is a bounded right D-module map on K(H) which is not completely bounded.  相似文献   
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Bloch Functions in Several Complex Variables, I   总被引:8,自引:0,他引:8  
Bloch functions on the unit disk are those analytic functionsf for which the quantity |f'(z)|(1 – |z|2) is bounded(for z in the disk). In this paper, Bloch functions on boundedhomogeneous domains in complex m-space are studied. The mainresult shows that many of the equivalent definitions of Blochfunctions on the unit disk are also equivalent in the generalsetting. Current Address: 39 Trinity College, Dublin 2, Ireland.  相似文献   
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