On the Nonexistence of Order Isomorphisms between the Sets of All Self-Adjoint and All Positive Definite Operators
Author
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-02-04
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We prove that there is no bijective map between the set of all positive definite operators and the set of all self-adjoint operators on a Hilbert space with dimension greater than 1 which preserves the usual order (the one coming from the concept of positive semidefiniteness) in both directions.
We conjecture that a similar assertion is true for general noncommutative C*-algebras and present a proof in the finite dimensional case.
American Psychological Association (APA)
Molnár, Lajos. 2015. On the Nonexistence of Order Isomorphisms between the Sets of All Self-Adjoint and All Positive Definite Operators. Abstract and Applied Analysis،Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1052045
Modern Language Association (MLA)
Molnár, Lajos. On the Nonexistence of Order Isomorphisms between the Sets of All Self-Adjoint and All Positive Definite Operators. Abstract and Applied Analysis No. 2015 (2015), pp.1-6.
https://search.emarefa.net/detail/BIM-1052045
American Medical Association (AMA)
Molnár, Lajos. On the Nonexistence of Order Isomorphisms between the Sets of All Self-Adjoint and All Positive Definite Operators. Abstract and Applied Analysis. 2015. Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1052045
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052045
