$$C^*$$-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
Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces
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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
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
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