MAXIMALITY OF THE ANALYTIC SUBALGEBRAS OF C^{*}-ALGEBRAS WITH FLOWS

- Journal title : Journal of the Korean Mathematical Society
- Volume 50, Issue 6, 2013, pp.1333-1348
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2013.50.6.1333

Title & Authors

MAXIMALITY OF THE ANALYTIC SUBALGEBRAS OF C^{*}-ALGEBRAS WITH FLOWS

Kishimoto, Akitaka;

Kishimoto, Akitaka;

Abstract

Given a faithful flow on a -algebra A, when A is -simple we will show that the closed subalgebra of A consisting of elements with non-negative Arveson spectra is maximal if and only if the crossed product of A by is simple. We will also show how the general case can be reduced to the -simple case, which roughly says that any flow with the above maximality is an extension of a trivial flow by a flow of the above type in the -simple case. We also propose a condition of essential maximality for such closed subalgebras.

Keywords

Arveson spectrum;maximal subalgebra;crossed product;

Language

English

References

2.

3.

S. Kawamura and J. Tomiyama, On subdiagonal algebras associated with flows in oper- ator algebras, J. Math. Soc. Japan 29 (1977), no. 1, 73-90.

4.

A. Kishimoto, Simple crossed products of C*-algebras by locally compact abelian groups, Yokohama Math. J. 28 (1980), no. 1-2, 69-85.

5.

A. Kishimoto, Universally weakly inner one-parameter automorphism groups of simple C*- algebras, Yokohama Math. J. 29 (1981), no. 2, 89-100.

6.

A. Kishimoto, Universally weakly inner one-parameter automorphism groups of C*-algebras, Yokohama Math. J. 30 (1982), no. 1-2, 141-149.

7.

8.

G. K. Pedersen, C*-Algebras and Their Automorphism Groups, Academic Press, 1979.