Isomorphisms of subalgebras of nest algebras

Author:
Fangyan Lu

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3883-3892

MSC (2000):
Primary 47L75, 47L35

Published electronically:
April 24, 2003

MathSciNet review:
1999937

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a subalgebra of a nest algebra . If contains all rank one operators in , then is said to be large; if the set of rank one operators in coincides with that in the Jacobson radical of , is said to be radical-type. In this paper, algebraic isomorphisms of large subalgebras and of radical-type subalgebras are characterized. Let be a nest of subspaces of a Hilbert space and be a subalgebra of the nest algebra associated to (). Let be an algebraic isomorphism from onto . It is proved that is spatial if one of the following occurs: (1) () is large and contains a masa; (2) () is large and closed; (3) () is a closed radical-type subalgebra and ( is quasi-continuous (i.e. the trivial elements of are limit points); (4) () is large and one of and is not quasi-continuous.

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Additional Information

**Fangyan Lu**

Affiliation:
Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China

Email:
fylu@pub.sz.jsinfo.net

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-07074-6

Keywords:
Algebraic isomorphisms,
nest algebras,
large subalgebras,
radical-type algebras,
rank one operators,
spatially implemented

Received by editor(s):
September 24, 2001

Received by editor(s) in revised form:
August 8, 2002

Published electronically:
April 24, 2003

Communicated by:
David R. Larson

Article copyright:
© Copyright 2003
American Mathematical Society