Journal article
Analyticity and flows in von Neumann algebras
Journal of functional analysis, Vol.29(2), pp.214-252
1978
DOI: 10.1016/0022-1236(78)90007-1
Abstract
Let
B
be a von Neumann algebra, let {
α
t
}
tεR
be an ultraweakly continuous one-parameter group of
∗-automorphisms of
B
, and let
U
be the set of all
A such that for each ϱ in
B
∗, the function
t →
ϱ(
α
t
(
A)) lies in
H
∞(
R
. Then
U
is an ultraweakly closed subalgebra of
B
containing the identity which is proper and non-self-adjoint if {
α
t
}
tεR
is not trivial. In this paper, a systematic investigation into the structure theory of
U
is begun. Two of the more note-worthy developments are these. First of all, conditions under which
U
is a subdiagonal algebra in
B
, in the sense of Arveson, are determined. The analysis provides a common perspective from which to view a large number of hitherto unrelated algebras. Second, the invariant subspace structure of
U
is determined and conditions under which
U
is a reductive subalgebra of
B
are found. These results are then used to produce examples where
U
is a proper, non-self-adjoint, reductive subalgebra of
B
. The examples do not answer the reductive algebra question, however, because although ultraweakly closed, the subalgebras are weakly dense in
B
.
Details
- Title: Subtitle
- Analyticity and flows in von Neumann algebras
- Creators
- Richard I Loebl - Department of Mathematics, Wayne State University, Detroit, Michigan 48202 U.S.APaul S Muhly - Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242 U.S.A
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.29(2), pp.214-252
- DOI
- 10.1016/0022-1236(78)90007-1
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 1978
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984083237102771
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