89 research outputs found
Uniqueness Theorems and Ideal Structure for Leavitt Path Algebras
We prove Leavitt path algebra versions of the two uniqueness theorems of
graph C*-algebras. We use these uniqueness theorems to analyze the ideal
structure of Leavitt path algebras and give necessary and sufficient conditions
for their simplicity. We also use these results to give a proof of the fact
that for any graph E the Leavitt path algebra embeds as a
dense *-subalgebra of the graph C*-algebra C*(E). This embedding has
consequences for graph C*-algebras, and we discuss how we obtain new
information concerning the construction of C*(E).Comment: 34 pages, uses XY-pic. New version comments: Some small typos
corrected. This is the final version to appear in the Journal of Algebr
Vector spaces with an order unit
We develop a theory of ordered *-vector spaces with an order unit. We prove
fundamental results concerning positive linear functionals and states, and we
show that the order (semi)norm on the space of self-adjoint elements admits
multiple extensions to an order (semi)norm on the entire space. We single out
three of these (semi)norms for further study and discuss their significance for
operator algebras and operator systems. In addition, we introduce a functorial
method for taking an ordered space with an order unit and forming an
Archimedean ordered space. We then use this process to describe an appropriate
notion of quotients in the category of Archimedean ordered spaces.Comment: 38 pages, uses XY-pic, Version 2 comments: minor typos corrected.;
Version 3 Comments: minor typos corrected; Version 4 Comments: minor typos
corrected, hypothesis of Archimedean added to Theorem 4.22, To appear in
Indiana Univ. Math.
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