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.

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.

Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most closely imitate finite-dimensional operator theory. In addition, compact operators are important in practice. We prove a spectral theorem for self-adjoint compact operators, which does not use broader discussions of properties of spectra, only using the Cauchy-Schwarz-Bunyakowsky inequality...

Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most closely imitate finite-dimensional operator theory. In addition, compact operators are important in practice. We prove a spectral theorem for self-adjoint compact operators, which does not use broader discussions of properties of spectra, only using the Cauchy-Schwarz-Bunyakowsky inequality...

We continue the study of the relationship between Dixmier traces and noncommutative residues initiated by A. Connes. The utility of the residue approach to Dixmier traces is shown by a characterisation of the noncommutative integral in Connes’ noncommutative geometry (for a wide class of Dixmier traces) as a generalised limit of vector states associated to the eigenvectors of a compact operator...

For the q-deformation Gq , 0 < q < 1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator Dq is a unitary twist of D considered as an element of Ug ⊗ Cl(g). The commutator of Dq with a regular function on Gq consists of two parts. One is a twist...