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The Symmetric Algebra of Quotients and its Bounded Analogue

  • Pere Ara
  • Martin Mathieu
Chapter
  • 304 Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

We now set up the scenario for local multipliers of C*-algebras. In the first section, the symmetric ring of quotients Q s (R) of a semiprime ring R is introduced and some of the basic properties of Q s (R), as well as of its centre C(R), called the extended centroid of R, will be studied. If R carries an involution, then this can be extended to Q s (R); this is the main advantage of the symmetric ring over other, one-sided rings of quotients. In the case of a C*-algebra A, Q s (A) becomes a *-algebra with positive-definite involution. Hence, it is possible to define order-bounded elements in the sense of Han- delman and Vidav and to distinguish the *-subalgebra Q b (A) of all bounded elements within Q s (A) (Section 2.2). Using the identity element as an order-unit, Q b (A)sa is an order-unit space and so Qb(A) is a pre- C*-algebra; its completion is the algebra of local multipliers of A, denoted by M loc (A) and introduced in Section 2.3.

Keywords

Prime Ring Functional Calculus Double Centraliser Dense Open Subset Semiprime Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2003

Authors and Affiliations

  • Pere Ara
    • 1
  • Martin Mathieu
    • 2
  1. 1.Departament de MatemàtiquesUniversitat Autónorna de BarcelonaBellaterraSpain
  2. 2.Department of Pure Mathematics School of Mathematics and PhysicsQueen’s University BelfastBelfastNorthern Ireland

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