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1 results

  • Operator Algebras with Contractive Approximate Identities

  • Yiu-Tung Poon, Zhong-Jin Ruan
  • Journal:
    Canadian Journal of Mathematics / Volume 46 / Issue 2 / 01 April 1994
    Published online by Cambridge University Press:
    20 November 2018, pp. 397-414
    Print publication:
    01 April 1994
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  • We study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.