Monotone operator functions on C*-algebras
(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:
https://lup.lub.lu.se/record/248976
- author
- Osaka, H ; Silvestrov, Sergei LU and Tomiyama, J
- organization
- publishing date
- 2005
- 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 Publishing
- 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
- 2016-04-01 16:19:54
- date last changed
- 2022-04-22 21:14:11
@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}},
keywords = {{operator monotone functions; subhomogeneous C*-algebra}},
language = {{eng}},
number = {{2}},
pages = {{181--196}},
publisher = {{World Scientific Publishing}},
series = {{International Journal of Mathematics}},
title = {{Monotone operator functions on C*-algebras}},
url = {{http://dx.doi.org/10.1142/S0129167X05002813}},
doi = {{10.1142/S0129167X05002813}},
volume = {{16}},
year = {{2005}},
}