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Several inequalities for an integral transform of positive operators in Hilbert spaces with applications

Cubo, 2023
For a continuous and positive function $w\left( \lambda \right) ,$ $\lambda >0$ and $\mu $ a positive measure on $(0,\infty )$ we consider the following integral transform % \begin{equation*} \mathcal{D}\left( w,\mu \right) \left( T\right) :=\int_{0}^{
S. S. Dragomir
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Gradient Inequalities for an Integral Transform of Positive Operators in Hilbert Spaces

Annales Mathematicae Silesianae, 2023
For a continuous and positive function w (λ) , λ > 0 and µ a positive measure on (0, ∞) we consider the following integral transform 𝒟(w,μ)(T):=∫0∞w(λ)(λ+T)-1dμ(λ),\mathcal{D}\left( {w,\mu } \right)\left( T \right): = \int_0^\infty {w\left( \lambda ...
Dragomir Silvestru Sever
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Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems. [PDF]