If 3C is a separable (complex) Hubert space, and A is a (bounded, linear) operator on 3C, then A is a commutator if there exist operators B and C on 3C such that 4 = BCCB. I t was shown by Wintner [8] and also by Wielandt [7] that no nonzero scalar multiple of the identity operator I on 3C is a commutator, and this was improved by Halmos [5] who showed that no operator of the form X / + C is a ...

Let L be a bounded linear Fredholm mapping of index zero, mapping a Banach space X into a Banach space 7. Then necessary and sufficient conditions for the solvability of the operator equation Lu = ƒ for ƒ e Y are well known. However the same satisfactory state of affairs does not hold for semilinear operator equations in which a compact nonlinear operator Nu is added to the right hand side of L...

We give an example of a non-compact, locally compact group G such that its Fourier–Stieltjes algebra B(G) is operator amenable. Furthermore, we characterize those G for which A * (G)—the spine of B(G) as introduced by M. Ilie and the second named author is operator amenable and show that A * (G) is operator weakly amenable for each G.

We give an example of a non-compact, locally compact group G such that its Fourier–Stieltjes algebra B(G) is operator amenable. Furthermore, we characterize those G for which A * (G)—the spine of B(G) as introduced by M. Ilie and the second named author—is operator amenable and show that A * (G) is operator weakly amenable for each G.