Monotone operator functions on C*algebras
(2005) In International Journal of Mathematics 16(2). p.181196 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:
http://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
 external identifiers

 wos:000227753900005
 scopus:14644405618
 ISSN
 0129167X
 DOI
 10.1142/S0129167X05002813
 language
 English
 LU publication?
 yes
 id
 4136023649eb449ca31ca835a3b7fd0d (old id 248976)
 date added to LUP
 20070820 09:12:20
 date last changed
 20170101 07:02:17
@article{4136023649eb449ca31ca835a3b7fd0d, 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 = {0129167X}, keyword = {operator monotone functions,subhomogeneous C*algebra}, language = {eng}, number = {2}, pages = {181196}, 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}, }