Advanced

Monotone operator functions on C*-algebras

Osaka, H; Silvestrov, Sergei LU and Tomiyama, J (2005) In International Journal of Mathematics 16(2). p.181-196
Abstract
The article is devoted to investigation of classes of functions monotone as functions on general C-*-algebras that are not necessarily the C-*-algebra of all bounded linear operators on a Hilbert space as in classical case of matrix and operator monotone functions. We show that for general C-*-algebras the classes of monotone functions coincide with the standard classes of matrix and operator monotone functions. For every class we give exact characterization of C-*-algebras with this class of monotone functions, providing at the same time a monotonicity characterization of subhomogeneous C-*-algebras. We use this result to generalize characterizations of commutativity of a C-*-algebra based on monotonicity conditions for a single function... (More)
The article is devoted to investigation of classes of functions monotone as functions on general C-*-algebras that are not necessarily the C-*-algebra of all bounded linear operators on a Hilbert space as in classical case of matrix and operator monotone functions. We show that for general C-*-algebras the classes of monotone functions coincide with the standard classes of matrix and operator monotone functions. For every class we give exact characterization of C-*-algebras with this class of monotone functions, providing at the same time a monotonicity characterization of subhomogeneous C-*-algebras. We use this result to generalize characterizations of commutativity of a C-*-algebra based on monotonicity conditions for a single function to characterizations of subhomogeneity. As a C-*-algebraic counterpart of standard matrix and operator monotone scaling, we investigate, by means of projective C-*-algebras and relation lifting, the existence of C-*-subalgebras of a given monotonicity class. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
operator monotone functions, subhomogeneous C*-algebra
in
International Journal of Mathematics
volume
16
issue
2
pages
181 - 196
publisher
World Scientific
external identifiers
  • wos:000227753900005
  • scopus:14644405618
ISSN
0129-167X
DOI
10.1142/S0129167X05002813
language
English
LU publication?
yes
id
41360236-49eb-449c-a31c-a835a3b7fd0d (old id 248976)
date added to LUP
2007-08-20 09:12:20
date last changed
2017-01-01 07:02:17
@article{41360236-49eb-449c-a31c-a835a3b7fd0d,
  abstract     = {The article is devoted to investigation of classes of functions monotone as functions on general C-*-algebras that are not necessarily the C-*-algebra of all bounded linear operators on a Hilbert space as in classical case of matrix and operator monotone functions. We show that for general C-*-algebras the classes of monotone functions coincide with the standard classes of matrix and operator monotone functions. For every class we give exact characterization of C-*-algebras with this class of monotone functions, providing at the same time a monotonicity characterization of subhomogeneous C-*-algebras. We use this result to generalize characterizations of commutativity of a C-*-algebra based on monotonicity conditions for a single function to characterizations of subhomogeneity. As a C-*-algebraic counterpart of standard matrix and operator monotone scaling, we investigate, by means of projective C-*-algebras and relation lifting, the existence of C-*-subalgebras of a given monotonicity class.},
  author       = {Osaka, H and Silvestrov, Sergei and Tomiyama, J},
  issn         = {0129-167X},
  keyword      = {operator monotone functions,subhomogeneous C*-algebra},
  language     = {eng},
  number       = {2},
  pages        = {181--196},
  publisher    = {World Scientific},
  series       = {International Journal of Mathematics},
  title        = {Monotone operator functions on C*-algebras},
  url          = {http://dx.doi.org/10.1142/S0129167X05002813},
  volume       = {16},
  year         = {2005},
}