Shorted operators and the structure of operators with numerical radius one

The theory of the shorted operator is used to prove that if w(T)1, then T can be written in the form T=2(I-C*C)^1/2C. Using this form, Ando has exhibited a matricial form for a unitary 2-dilation of T.     

The general Stone-Weierstrass problem and extremal completely positive maps

Let A be a C*-algebra with identity e and let B be a C*-subalgebra of A that contains e. We show that if B separates the pure states of A, then, for each n, B also separates the set ECP(A,ⁿ;I) of extremal completely positive unital maps of A into ⁿ, thus giving another equivalent condition for the general Stone-Weierstrass conjecture for C*-algebras.     

The ferrous verdoheme-heme oxygenase complex is six-coordinate and low-spin

A biosynthetic and enzymatic method was developed for the preparation of 13C-labeled verdoheme, which permits the 13C NMR spectroscopic characterization of this elusive intermediate in the heme oxidation path catalyzed by the enzyme heme oxygenase. The 13C NMR data indicate that the ferrous verdoheme complex of Neisseria meningitides heme oxygenase is hexacoordinate and diamagnetic, with a proximal histidine and likely a distal hydroxide as axial ligands. The coordination number and spin state of the ferrous verdoheme-heme oxygenase complex is in stark contrast to the pentacoordinate and paramagnetic nature of the heme-heme oxygenase complex and heme centers in general.     

Domino Nitro Reduction-Friedländer Heterocyclization for the Preparation of Quinolines

The Friedländer synthesis offers efficient access to substituted quinolines from 2-aminobenzaldehydes and activated ketones in the presence of a base. The disadvantage of this procedure lies in the fact that relatively few 2-aminobenzaldehyde derivatives are readily available. To overcome this problem, we report a modification of this process involving the in situ reduction of 2-nitrobenzaldehydes with Fe/AcOH in the presence of active methylene compounds (AMCs) to produce substituted quinolines in high yields. The conditions are mild enough to tolerate a wide range of functionality in both reacting partners and promote reactions not only with phenyl and benzyl ketones, but also with β-keto-esters, β-keto-nitriles, β-keto-sulfones and β-diketones. The reaction of 2-nitroaromatic ketones with unsymmetrical AMCs is less reliable, giving a competitive formation of substituted quinolin-2(1H)-ones from the cyclization of the Z Knoevenagel intermediate which appears to be favored when certain large groups are adjacent to the AMC ketone carbonyl.     

Diastereoselective synthesis of linear‐fused tricyclic nitrogen heterocycles by a tandem reduction‐reductive amination reaction

A two‐step diastereoselective synthesis of linear‐fused tricyclic nitrogen heterocycles has been developed from cyclic β‐ketoesters. The cyclization substrates are readily prepared by alkylation of the methyl 2‐oxo‐cycloalkanecarboxylates with 2‐nitrobenzyl bromide. Hydrogenation of these substrates initiates a reaction sequence involving (1) reduction of the aromatic nitro group, (2) condensation of the resulting hydroxyl‐amine or aniline nitrogen with the cycloalkanone and (3) reduction of the imine. The products are isolated in high yield as single diastereomers having the trans‐fused ring junction. The observed selectivity is rationalized in terms of a steric effect imposed by the ester group in the final reductive amination step which directs the incoming hydrogen to the opposite face of the molecule. By comparison, reductive cyclizations of substrates lacking the stereodirecting ester group give mixtures of cis and trans products with a preference for the cis‐fused heterocycle.     

Spacer Control of Directionality in Supramolecular Helicates Using an Inexpensive Approach

Careful selection of the spacer group used to separate the metal-binding domains allows control of the directionality in a helix; self-assembly leads uniquely to a double-helical cation with a head-to-tail (HT) configuration (shown schematically) in both the solid state and solution.     

Prime JB*‐Triples and Extreme Dual Ball Density

Properties of the extreme points ∂_e(E*₁) of the closed dual ball E*₁ of a JB*‐triple E are studied. It is shown that the canonical mapping from ∂_e(E*₁) onto the structure space, Prim (E), of primitive M‐ideals of E is an open mapping. This property is utilised to show that ∂_e(E*₁) is weak* dense in E*₁ if and only if E is an infinite dimensional Hilbert space, an infinite dimensional spin factor or E is prime with zero socle.     

Classification of sequentially weakly continuous $JB^*$-triples

Let D be the open unit ball of a -triple A and let Aut(D) be the group of all biholomorphic automorphisms of D. It is shown that every element of Aut(D) is sequentially weakly continuous if and only if every primitive ideal of A is a maximal closed ideal and is a type I -triple without infinite-spin part. Implications for general structure theory are explored. In particular, it is deduced that every -triple A contains a smallest ideal J for which the sequentially weakly continuous biholomorphic automorphisms of the open unit ball of A/J are all linear. Received August 27, 1998; in final form February 10, 1999