Abstract/Details

Properties of nest algebras

Pan, Zhidong. 
 University of Connecticut ProQuest Dissertations Publishing,  1992. 9300941.

Abstract (summary)

Let H be a Hilbert space and B(H) be the set of all bounded linear operators on H. A nest ${\cal N}$ in H is a totally ordered set of orthogonal projections. The corresponding nest algebra $Alg{\cal N}$ is $$Alg{\cal N} \equiv \{T \in B(H) \mid PTP = TP, \forall P \in {\cal N}\}.$$A nest is said to be finite if it contains only finitely many orthogonal projections.

In this dissertation, we show that ${\cal N}$ is finite if and only if $Alg{\cal N} + (Alg{\cal N})\sp* = B(H)$ if and only if $Alg{\cal N}$ is complemented in $B(H)$ as a subspace of $B(H),$ which is also equivalent to one of the following: (UNFORMATTED TABLE OR EQUATION FOLLOWS)$$\eqalign{&(1)\quad Alg{\cal N} + (Alg{\cal N})\sp*\ \rm is\ an\ algebra.\cr&(2)\quad Alg{\cal N} + (Alg{\cal N})\sp*\ {\rm is\ norm\ closed\ in}\ B(H).\cr&(3)\quad Alg{\cal N} + (Alg{\cal N})\sp*\ {\rm is\ norm\ dense\ in}\ B(H).\cr}$$(TABLE/EQUATION ENDS)

We also investigate the homotopy of invertibles in nest algebras.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Properties of nest algebras
Author
Pan, Zhidong
Number of pages
68
Degree date
1992
School code
0056
Source
DAI-B 53/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-208-48328-2
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9300941
ProQuest document ID
303977054
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303977054/abstract