$L^p$-Spaces as Quasi *-Algebras

F. Bagarello; C. Trapani

$L^p$-Spaces as Quasi *-Algebras

funct-an 2008-02-03 v1 Operator Algebras

Authors: F. Bagarello , C. Trapani

Abstract

The Banach space $L^p(X,\mu)$ , for $X$ a compact Hausdorff measure space, is considered as a special kind of quasi *-algebra (called CQ*-algebra) over the C*-algebra $C(X)$ of continuous functions on $X$ . It is shown that, for $p \geq 2$ , $(L^p(X,\mu), C(X))$ is *-semisimple (in a generalized sense). Some consequences of this fact are derived.

Cite

@article{arxiv.funct-an/9410002,
  title  = {$L^p$-Spaces as Quasi *-Algebras},
  author = {F. Bagarello and C. Trapani},
  journal= {arXiv preprint arXiv:funct-an/9410002},
  year   = {2008}
}

Comments

14 pages, AmsLatex

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