Operator inequalities, geodesics and interpolation
Operator inequalities of Jensen type
We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, then [...] for all operators Ci such that [...] (i=1 , ... , n) for some scalar M ≥ 0, where [...] and [...]
Operator-valued inner product and operator inequalities.
Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces
Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral of continuous complex valued integrands defined on the complex unit circle and various subclasses of integrators of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.
Ostrowski's type inequalities for continuous functions of selfadjoint operators on Hilbert spaces: a survey of recent results.
Polar decomposition approach to Reid's inequality.
Positivity of operator-matrices of Hua-type.
Powers of class operators.
Powers of -hyponormal operators.
Quantum states satisfying classical probability constraints
For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify bipartite state properties sufficient for the validity of a classical CHSH-form inequality and the perfect correlation form of the original Bell inequality for any bounded quantum observables. We also introduce a new general condition on a bipartite state and quantum...
Remark on an operator inequality
Reverse inequalities on chaotically geometric mean via Specht ratio. II.
Reverse of the grand Furuta inequality and its applications.
Some inequalities for commutators and an application to spectral variation.
Some operator inequalities
Some results on operator means and shorted operators.
Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces.
Some vector inequalities for continuous functions of self-adjoint operators in Hilbert spaces.
Spectral dominance and Young's inequality in type III factors.
Squaring a reverse AM-GM inequality
Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.