TY - JOUR
AU - Pavlov, Alexander
AU - Pennig, Ulrich
AU - Schick, Thomas
PY - 2011/09/01
Y2 - 2024/05/29
TI - Quasi-multipliers of Hilbert and Banach $C^*$-bimodules
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 109
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-15178
UR - https://www.mscand.dk/article/view/15178
SP - 71-92
AB - Quasi-multipliers for a Hilbert $C^*$-bimodule $V$ were introduced by L. G. Brown, J. A. Mingo, and N.-T. Shen [3] as a certain subset of the Banach bidual module $V^{**}$. We give another (equivalent) definition of quasi-multipliers for Hilbert $C^*$-bimodules using the centralizer approach and then show that quasi-multipliers are, in fact, universal (maximal) objects of a certain category. We also introduce quasi-multipliers for bimodules in Kasparov's sense and even for Banach bimodules over $C^*$-algebras, provided these $C^*$-algebras act non-degenerately. A topological picture of quasi-multipliers via the quasi-strict topology is given. Finally, we describe quasi-multipliers in two main situations: for the standard Hilbert bimodule $l_2(A)$ and for bimodules of sections of Hilbert $C^*$-bimodule bundles over locally compact spaces.
ER -