scholarly journals On characterization of operator monotone functions

2015 ◽  
Vol 487 ◽  
pp. 260-267 ◽  
Author(s):  
Dinh Trung Hoa
Keyword(s):  
Monotone Functions ◽  
Operator Monotone ◽  
Operator Monotone Functions

MONOTONE OPERATOR FUNCTIONS ON C*-ALGEBRAS

2005 ◽  
Vol 16 (02) ◽  
pp. 181-196 ◽  
Author(s):  
HIROYUKI OSAKA ◽  
SERGEI SILVESTROV ◽  
JUN TOMIYAMA
Keyword(s):  
Classical Case ◽  
Linear Operators ◽  
Monotone Functions ◽  
Bounded Linear ◽  
C Algebra ◽  
C Algebras ◽  
Operator Monotone ◽  
Operator Functions ◽  
Operator Monotone Functions

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.

scholarly journals Kwong matrices and operator monotone functions on $(0,1)$

2014 ◽  
Vol 5 (1) ◽  
pp. 121-127 ◽  
Author(s):  
Juri Morishita ◽  
Takashi Sano ◽  
Shintaro Tachibana
Keyword(s):  
Monotone Functions ◽  
Operator Monotone ◽  
Operator Monotone Functions

scholarly journals Strengthened convexity of positive operator monotone decreasing functions

2020 ◽  
Vol 126 (3) ◽  
pp. 559-567
Author(s):  
Megumi Kirihata ◽  
Makoto Yamashita
Keyword(s):  
Logarithmic Function ◽  
Monotone Functions ◽  
Real Numbers ◽  
Positive Real ◽  
Positive Maps ◽  
Operator Monotone ◽  
Strengthened Form ◽  
Operator Monotone Functions ◽  
Positive Functions ◽  
Decreasing Functions

We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map), and functional calculus by operator monotone functions defined on the positive real numbers instead of the logarithmic function.

scholarly journals A new class of operator monotone functions via operator means

2016 ◽  
Vol 64 (12) ◽  
pp. 2463-2473 ◽  
Author(s):  
Rajinder Pal ◽  
Mandeep Singh ◽  
Mohammad Sal Moslehian ◽  
Jaspal Singh Aujla
Keyword(s):  
Monotone Functions ◽  
New Class ◽  
Operator Monotone ◽  
Operator Means ◽  
Operator Monotone Functions
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