![](/images/graphics-bg.png)
Strictly Cyclic Functionals, Reflexivity, and Hereditary Reflexivity of Operator Algebras
Joint Authors
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-09
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
This paper is concerned with strictly cyclic functionals of operator algebras on Banach spaces.
It is shown that if X is a reflexive Banach space and A is a norm-closed semisimple abelian subalgebra of B(X) with a strictly cyclic functional f∈X∗, then A is reflexive and hereditarily reflexive.
Moreover, we construct a semisimple abelian operator algebra having a strictly cyclic functional but having no strictly cyclic vectors.
The hereditary reflexivity of an algbra of this type can follow from theorems in this paper, but does not follow directly from the known theorems that, if a strictly cyclic operator algebra on Banach spaces is semisimple and abelian, then it is a hereditarily reflexive algebra.
American Psychological Association (APA)
Chen, Quanyuan& Fang, Xiaochun. 2012. Strictly Cyclic Functionals, Reflexivity, and Hereditary Reflexivity of Operator Algebras. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-471937
Modern Language Association (MLA)
Chen, Quanyuan& Fang, Xiaochun. Strictly Cyclic Functionals, Reflexivity, and Hereditary Reflexivity of Operator Algebras. Abstract and Applied Analysis No. 2012 (2012), pp.1-12.
https://search.emarefa.net/detail/BIM-471937
American Medical Association (AMA)
Chen, Quanyuan& Fang, Xiaochun. Strictly Cyclic Functionals, Reflexivity, and Hereditary Reflexivity of Operator Algebras. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-471937
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-471937