Property (w) and perturbations III
AbstractThe property (w) is a variant of Weyl's theorem, for a bounded operator T acting on a Banach space. In this note we consider the preservation of property (w) under a finite rank perturbation commuting with T, whenever T is polaroid, or T has analytical core K(λ0I−T)={0} for some λ0∈C. The preservation of property (w) is also studied under commuting nilpotent or under injective quasi-nilpotent perturbations. The theory is exemplified in the case of some special classes of operators.
Mono- and di-nuclear 2,3-diazabutadiene and 2-azabutadiene complexes of Rhenium(I): Syntheses, luminescence spectra and X-ray structures
Abstract Treatment of [Re(CO)3(THF)(μ-Br)]2 with 4,4-dichloro-1,1-diphenyl-2-azabuta-1,3-diene [Cl2C C(H)–N CPh2] (1a) yields the di-nuclear benzophenone azine-bridged compound [(OC)3Re(μ-Ph2C N–N CPh2)(μ-Br)2Re(CO)3] (2a), albeit in low yield. Alternatively, compounds [(OC)3Re(μ-Ph2C N–N CPh2)(μ-X)2Re(CO)3] (2a,b) (X = Br, Cl) are obtained in high yields by direct reaction of [Re(CO)3(THF)(μ-Br)]2 or [Re(CO)5Cl] with benzophenone azine. Nucleophilic attack of NaSPh on 1a affords the 2-azabutadiene derivative [(PhS)(Cl)C C(H)–N CPh2] (1b), which upon reaction with [Re(CO)3(THF)(μ-Br)]2 forms the S,N-chelate complex fac-[(OC)3ReBr{(PhS)(Cl)C C(H)–N CPh2}] (3). The crystal structures of 1b, 2…
(2,2‐Dibromovinyl)ferrocene as a Building Block for the Assembly of Heterodinuclear Complexes – Preparation of an σ‐Alkenylpalladium Complex and Dimetallic Dithioether Complexes
The oxidative addition of (2,2-dibromovinyl)ferrocene [Br2C=C(H)–Fc] (1) to [Pd(PPh3)4] yields the heterodinuclear σ-alkenyl complex trans-[{Pd(Br)(PPh3)2}–C(Br)=C(H)–Fc] (2). Nucleophilic attack of sodium thiolates on 1 unexpectedly affords the vinyl thioether derivatives (Z)-[(RS)(H)C=C(H)–Fc] (4a: R = Ph; 4b: R = tBu; 4c: R = Et). Complexes 4a and 4c can also be prepared by addition of NaSR across the triple bond of Fc–C≡C–H (3). Addition of an excess of NaSR to 1 affords the dithioether derivatives (Z)-[(RS)(H)C=C(SR)–Fc] (5a: R = Ph; 5b: R = p-tolyl; 5c: R = Et). An addition/elimination sequence is suggested to account for this surprising result. The yield of 5c is very low due to a co…