Refining the Hermite-Hadamard inequalities for operator convex maps in multiple operator variables

2021 ◽  
Author(s):  
Mustapha Raïssouli
Keyword(s):  
Operator Convex ◽  
Multiple Operator

scholarly journals Some Hermite-Hadamard type inequalities for operator convex functions and positive maps

2019 ◽  
Vol 7 (1) ◽  
pp. 38-51 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Power Function ◽  
Convex Functions ◽  
Positive Maps ◽  
Operator Convex ◽  
Operator Convex Functions

Abstract In this paper we establish some inequalities of Hermite-Hadamard type for operator convex functions and positive maps. Applications for power function and logarithm are also provided.

Multiple-Operator Discriminandum for Classroom Use

1972 ◽  
Vol 35 (3) ◽  
pp. 972-974
Author(s):  
E. Shimoff
Keyword(s):  
Classroom Behavior ◽  
Discriminative Stimuli ◽  
Classroom Use ◽  
Multiple Operator

A device is described which allows students to present discriminative stimuli to an instructor during a lecture Explicit and immediare reinforcement of the instructor's appropriate classroom behavior increased clarity and informativeness of lectures

scholarly journals Operator Integrals, Spectral Shift, and Spectral Flow

2009 ◽  
Vol 61 (2) ◽  
pp. 241-263 ◽  
Author(s):  
N. A. Azamov ◽  
A. L. Carey ◽  
P. G. Dodds ◽  
F. A. Sukochev
Keyword(s):  
Von Neumann Algebras ◽  
Spectral Shift ◽  
Shift Function ◽  
Spectral Flow ◽  
Spectral Shift Function ◽  
Spectral Measures ◽  
Unbounded Operators ◽  
Von Neumann ◽  
Operator Functions ◽  
Multiple Operator

Abstract. We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fréchet differentiation of operator functions that sharpen existing results, and establish the Birman–Solomyak representation of the spectral shift function of M.G. Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow.

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