Quantum resource theories provide a diverse and powerful framework for extensively studying the phenomena in quantum physics. coherence, resource, is basic ingredient many information tasks. It subject of broad current interest information, new concepts have been introduced generalized since its establishment. Here we show that block coherence can be transformed into entanglement via block-inco...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Abstract. The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with particular properties and motivates our results. We find a necessary and sufficient condition under which any positive finite-rank operator B can be e...

The powerset operator, P, is an operator which (1) sends sets to sets,(2) is defined by a positive formula and (3) raises the cardinality of its argument, i.e., |P(x)| > |x|. As a consequence of (3), P has a proper class as least fixed point (the universe itself). In this paper we address the questions: (a) How does P contribute to the generation of the class of all positive operators? (b) Are ...

let  be a hilbert space of functions analytic on a plane domain  such that for every  in  the functional of evaluation at  is bounded. assume further that  contains the constants and admits multiplication by the independent variable , , as a bounded operator. we give sufficient conditions for  to be reflexive for all positive integers .