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Module homomorphisms and multipliers on locally compact quantum groups

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
359
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2009.03.059
Keywords
  • Locally Compact Quantum Group
  • Module Homomorphism
  • Wendel'S Theorem
  • Hopf–Von Neumann Algebra
  • Multiplier
  • Topological Centre
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract For a Banach algebra A with a bounded approximate identity, we investigate the A-module homomorphisms of certain introverted subspaces of A ∗ , and show that all A-module homomorphisms of A ∗ are normal if and only if A is an ideal of A ∗ ∗ . We obtain some characterizations of compactness and discreteness for a locally compact quantum group G . Furthermore, in the co-amenable case we prove that the multiplier algebra of L 1 ( G ) can be identified with M ( G ) . As a consequence, we prove that G is compact if and only if LUC ( G ) = WAP ( G ) and M ( G ) ≅ Z ( LUC ( G ) ∗ ) ; which partially answer a problem raised by Volker Runde.

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