In \cite{Tre_PSI20} we introduce the concept of a $\mu$-norm for bounded operator in Hilbert space. The main motivation is extension measure entropy to case quantum systems. this paper recall basic results from and present further on $\mu$-norm. More precisely, specify three classes unitary operators which generates bistochastic operator. We plan use latter construction entropy.

The recent development of the infrared cameras, the technologies of detection and tracking the target are under progress in the surveillance field, intelligent robot field, and the military field. Detection of infrared threat in IR defense systems are very important to use IR cameras. Many scholars have paid much attention to the study on spatial and temporal detections. Existing methods are fo...

We prove that for the relative entropy of faithful normal states φ and ω on the von Neumann algebra M the formula S(φ,ω) = sup{ω(Λ)-logφ(/): h = h*eM] holds. In general von Neumann algebras the relative entropy was defined and investigated by Araki [1, 3]. After Lieb had proved the joint convexity of the relative entropy in the type / case [10] several proofs appeared in the literature and they...

It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spe...