Automorphisms Inner in the Local Multiplier Algebra and Connes Spectrum

We obtain some results that relate the Connes spectrum with the innerness of automorphisms in the fixed point local multiplier algebra. The results are variants and/or extensions of corresponding results of Olesen, Pedersen and Stormer [6], [7], [9] and Ara and Mathieu [1] to the case of local multiplier algebras.