$$C^*$$-Extreme Points of Positive Operator Valued Measures and Unital Completely Positive Maps
Sign Up to like & getrecommendations! Published in 2021 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-021-04245-1
Abstract: We study the quantum ($C^*$) convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, $C^*$-extreme points of normalized POVMs on… read more here.
Keywords: unital completely; valued measures; operator valued; extreme points ... See more keywords
From Classical to Quantum: Polymorphisms in Non-Commutative Probability
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DOI: 10.1007/s11785-025-01837-w
Abstract: We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels are scalar valued.… read more here.
Keywords: operator valued; non commutative; classical quantum; theory ... See more keywords
Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Pseudo-Differential Operators and Applications"
DOI: 10.1007/s11868-017-0224-x
Abstract: In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are of limited smoothness… read more here.
Keywords: besov spaces; mapping properties; operator valued; pseudodifferential operators ... See more keywords
Operator-valued operators that are associated to vector-valued operators
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.04.040
Abstract: This paper is motivated by a long-standing conjecture of Dinculeanu from 1967. Let X and Y be Banach spaces and let Ω be a compact Hausdorff space. Dinculeanu conjectured that there exist operators S∈L(C(Ω),L(X,Y))S∈L(C(Ω),L(X,Y)) which… read more here.
Keywords: associated vector; operators associated; vector valued; operator valued ... See more keywords
Two constructions of approximately symmetric informationally complete positive operator-valued measures
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DOI: 10.1063/1.4985153
Abstract: Symmetric informationally complete positive operator-valued measures (SIC-POVMs) have many applications in quantum information. However, it is not easy to construct SIC-POVMs and there are only a few known classes of them, and we do not… read more here.
Keywords: informationally complete; complete positive; valued measures; positive operator ... See more keywords
Quantum steering with positive operator valued measures
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/aad115
Abstract: We address the problem of quantum nonlocality with positive operator valued measures (POVM) in the context of Einstein-Podolsky-Rosen quantum steering. We show that, given a candidate for local hidden state (LHS) ensemble, the problem of… read more here.
Keywords: valued measures; operator valued; quantum steering; positive operator ... See more keywords
Operator-valued zeta functions and Fourier analysis
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DOI: 10.1088/1751-8121/ab25fa
Abstract: The Riemann zeta function $\zeta(s)$ is defined as the infinite sum $\sum_{n=1}^\infty n^{-s}$, which converges when ${\rm Re}\,s>1$. The Riemann hypothesis asserts that the nontrivial zeros of $\zeta(s)$ lie on the line ${\rm Re}\,s= \frac{1}{2}$.… read more here.
Keywords: valued zeta; zeta functions; analytic continuation; operator valued ... See more keywords
On operator-valued infinitesimal Boolean and monotone independence
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DOI: 10.1142/s0219025721500193
Abstract: We introduce the notion of operator-valued infinitesimal (OVI) Boolean independence and OVI monotone independence. Then we show that OVI Boolean (respectively, monotone) independence is equivalent to the operator-valued (OV) Boolean (respectively, monotone) independence over an… read more here.
Keywords: operator valued; valued infinitesimal; monotone independence; boolean monotone ... See more keywords
Characterizing the R-duality of g-frames
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-019-2022-x
Abstract: In this paper, we define the g-Riesz-dual of a given special operator-valued sequence with respect to g-orthonormal bases for a separable Hilbert space. We demonstrate that the g-R-dual keeps some synchronous frame properties with the… read more here.
Keywords: operator valued; characterizing duality; valued sequence; duality frames ... See more keywords