Multipliers, Self-Induced and Dual Banach Algebras
By Matthew Daws. 2010
58 citations recorded by the source corpus.
In the first part of the paper, we present a short survey of the theory of multipliers, or double centralisers, of Banach algebras and completely contractive Banach algebras. Our approach is very algebraic: this is a deliberate attempt to separate essentially algebraic arguments from topological arguments. We concentrate upon the problem of how to extend module actions, and homomorphisms, from algebras to multiplier algebras. We then consider the special cases when we have a bounded approximate identity, and when our algebra is self-induced. In the second part of the paper, we mainly concentrate upon dual Banach algebras. We provide a simple criterion for when a multiplier algebra is a dual Banach algebra. This is applied to show that the multiplier algebra of the convolution algebra of a locally compact quantum group is always a dual Banach algebra. We also study this problem within the framework of abstract Pontryagin duality, and show that we construct the same weak$^*$-topology. We explore the notion of a Hopf convolution algebra, and show that in many cases, the use of the extended Haagerup tensor product can be replaced by a multiplier algebra.
Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2a5d03e788387b2f1645ea5175e04dbcb9b47ae4
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In Algebra and Number Theory
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Citations in the corpus
- Approximation properties for free orthogonal and free unitary quantum groups (2011, background): “ra of Gcan be isometrically identified with a closed subspace of A∗ via the dual pairing (2.3) hx,ωi = hω,πh(x)i, (x∈ A,ω∈ L1(G)). With this identification, L1(G) is a closed two-sided ideal in A∗ (see [17], [24, Page 913-914]). 3 Definition 2.1. An (n-dimensional) corepresentation of a CQG G = (A,∆) i”