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## OPERATOR CONNECTIONS AND BOREL MEASURES ON THE UNIT INTERVAL

Citations: | 2 - 2 self |

### Citations

753 |
Matrix analysis
- Bhatia
- 1997
(Show Context)
Citation Context ...(e.g. [2], [10]) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is introduced in [11]; see also =-=[4]-=-, [7], [8]. A continuous real-valued function f on an interval I is called an operator monotone function if, for all Hermitian operators A,B ∈ B(H) whose spectrums are contained in I and for all Hilbe... |

103 |
Means of positive linear operators
- Kubo, Ando
- 1980
(Show Context)
Citation Context ...operator monotone function, Borel measure AMS subject classifications. 46G10, 47A63, 47A64 1. Introduction. A general theory of connections and means for positive operators was given by Kubo and Ando =-=[9]-=-. Let B(H) be the von Neumann algebra of bounded linear operators on a Hilbert space H . The set of positive operators on H is denoted by B(H)+. For Hermitian operators A,B ∈ B(H), the partial order A... |

89 |
Concavity of certain maps on positive definite matrices and applications to Hadamard products
- Ando
- 1979
(Show Context)
Citation Context ... A !tB = [(1− t)A −1 + tB−1]−1 • logarithmic mean: (A,B) 7→ A1/2f(A−1/2BA−1/2)A1/2 where f : R+ → R+, f(x) = (x− 1)/ logx. This axiomatic approach has many applications in operator inequalities (e.g. =-=[3]-=-, [6], [12]), operator equations (e.g. [2], [10]) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept... |

85 |
monotone Matrixfunktionen
- Uber
- 1934
(Show Context)
Citation Context ...ator equations (e.g. [2], [10]) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is introduced in =-=[11]-=-; see also [4], [7], [8]. A continuous real-valued function f on an interval I is called an operator monotone function if, for all Hermitian operators A,B ∈ B(H) whose spectrums are contained in I and... |

22 |
Matrix Analysis: Matrix Monotone Functions
- Hiai
- 2010
(Show Context)
Citation Context ... [2], [10]) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is introduced in [11]; see also [4], =-=[7]-=-, [8]. A continuous real-valued function f on an interval I is called an operator monotone function if, for all Hermitian operators A,B ∈ B(H) whose spectrums are contained in I and for all Hilbert sp... |

19 |
Series and parallel addition of matrices
- Anderson, Duffin
- 1969
(Show Context)
Citation Context ...and the right-trivial mean (A,B) 7→ B. Typical examples of a connection are the sum (A,B) 7→ A+B and the parallel sum A : B = (A−1 +B−1)−1, A,B > 0, the latter being introduced by Anderson and Duffin =-=[1]-=-. A mean is a connection σ with normalized condition I σ I = I or, equivalently, fixed-point property Aσ A = A ∗Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology La... |

5 |
On Ando–Li–Mathias geometric mean equations
- Lim
(Show Context)
Citation Context ...an: (A,B) 7→ A1/2f(A−1/2BA−1/2)A1/2 where f : R+ → R+, f(x) = (x− 1)/ logx. This axiomatic approach has many applications in operator inequalities (e.g. [3], [6], [12]), operator equations (e.g. [2], =-=[10]-=-) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is introduced in [11]; see also [4], [7], [8]. ... |

2 |
Operator means and the relative operator entropy
- Fujii
- 1992
(Show Context)
Citation Context .../2)A1/2 where f : R+ → R+, f(x) = (x− 1)/ logx. This axiomatic approach has many applications in operator inequalities (e.g. [3], [6], [12]), operator equations (e.g. [2], [10]) and operator entropy (=-=[5]-=-). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is introduced in [11]; see also [4], [7], [8]. A continuous real-valued fu... |

2 |
A proof via operator means of an order preserving inequality
- Furuta
(Show Context)
Citation Context ...B = [(1− t)A −1 + tB−1]−1 • logarithmic mean: (A,B) 7→ A1/2f(A−1/2BA−1/2)A1/2 where f : R+ → R+, f(x) = (x− 1)/ logx. This axiomatic approach has many applications in operator inequalities (e.g. [3], =-=[6]-=-, [12]), operator equations (e.g. [2], [10]) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is i... |

2 |
Operator versions of some classical inequalities
- Mond, Pečarić, et al.
- 1997
(Show Context)
Citation Context ...(1− t)A −1 + tB−1]−1 • logarithmic mean: (A,B) 7→ A1/2f(A−1/2BA−1/2)A1/2 where f : R+ → R+, f(x) = (x− 1)/ logx. This axiomatic approach has many applications in operator inequalities (e.g. [3], [6], =-=[12]-=-), operator equations (e.g. [2], [10]) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is introdu... |

1 | Positive solutions to X = A − BX−1B - Anderson, Morley, et al. - 1990 |

1 |
spaces and linear operators
- Hilbert
- 1995
(Show Context)
Citation Context ... [10]) and operator entropy ([5]). A fundamental tool of Kubo-Ando theory of connections and means is the theory of operator monotone functions. This concept is introduced in [11]; see also [4], [7], =-=[8]-=-. A continuous real-valued function f on an interval I is called an operator monotone function if, for all Hermitian operators A,B ∈ B(H) whose spectrums are contained in I and for all Hilbert spaces ... |