Maximality of the analytic subalgebras of C*-algebras with flows
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Given a faithful flow α on a C∗-algebra A, when A is α-simple we will show that the closed subalgebra of A consisting of elementswith non-negative Arveson spectra is maximal if and only if the crossedproduct of A by α is simple. We will also show how the general case canbe reduced to the α-simple case, which roughly says that any flow withthe above maximality is an extension of a trivial flow by a flow of theabove type in the α-simple case. We also propose a condition of essentialmaximality for such closed subalgebras.
Abstract
Given a faithful flow α on a C∗-algebra A, when A is α-simple we will show that the closed subalgebra of A consisting of elementswith non-negative Arveson spectra is maximal if and only if the crossedproduct of A by α is simple. We will also show how the general case canbe reduced to the α-simple case, which roughly says that any flow withthe above maximality is an extension of a trivial flow by a flow of theabove type in the α-simple case. We also propose a condition of essentialmaximality for such closed subalgebras.
참고문헌 (11)
- W. B. Arveson, "Analyticity in operator algebras", Amer. J. Math, 89, pp.578~642 (1967)
- W. B. Arveson, "On groups of automorphisms of operator algebras", J. Funct. Anal, 15, pp.217~243 (1974)
- S. Kawamura, "On subdiagonal algebras associated with flows in oper- ator algebras", J. Math. Soc. Japan, 29(1), pp.73~90 (1977)
- A. Kishimoto, "Simple crossed products of C* -algebras by locally compact abelian groups", Yokohama Math. J, 28(1-2), pp.69~85 (1980)
- A. Kishimoto, "Universally weakly inner one-parameter automorphism groups of simple C*- algebras", Yokohama Math. J, 29(2), pp.89~100 (1981)
- A. Kishimoto, "Universally weakly inner one-parameter automorphism groups of C*-algebras", Yokohama Math. J, 30(1-2), pp.141~149 (1982)
- A. Kishimoto, "C*-crossed products by R. II", Publ. Res. Inst. Math. Sci, 45(2), pp.451~473 (2009)
- G. K. Pedersen, "C*-Algebras and Their Automorphism Groups" (1979), Academic Press
- C. Peligrad, "Maximal subalgebras of C*-algebras associated with periodic flows", J. Funct. Anal, 262(8), pp.3626~3637 (2012)
- B. Solel, "Maximality of analytic operator algebras", Israel J. Math, 62(1), pp.63~89 (1988)
- J. Wermer, "On algebras of continuous functions", Proc. Amer. Math. Soc, 4, pp.866~899 (1953)