• Corpus ID: 119126191

Semispectral Measures and Feller markov Kernels

@article{Beneduci2012SemispectralMA,
  title={Semispectral Measures and Feller markov Kernels},
  author={Roberto Beneduci},
  journal={arXiv: Functional Analysis},
  year={2012}
}
  • R. Beneduci
  • Published 30 June 2012
  • Mathematics
  • arXiv: Functional Analysis
We give a characterization of commutative semispectral measures by means of Feller and Strong Feller Markov kernels. In particular: {itemize} we show that a semispectral measure $F$ is commutative if and only if there exist a self-adjoint operator $A$ and a Markov kernel $\mu_{(\cdot)}(\cdot):\Gamma\times\mathcal{B}(\mathbb{R})\to[0,1]$, $\Gamma\subset\sigma(A)$, $E(\Gamma)=\mathbf{1}$, such that $$F(\Delta)=\int_{\Gamma}\mu_{\Delta}(\lambda)\,dE_{\lambda},$$ \noindent and $\mu_{(\Delta)}$ is… 
Joint measurability through Naimark's theorem
We use Naimark's dilation theorem in order to characterize the joint measurability of two POVMs. Then, we analyze the joint measurability of two commutative POVMs $F_1$ and $F_2$ which are the
Uniform Continuity of POVMs
Recently a characterization of uniformly continuous POVMs and a necessary condition for a uniformly continuous POVM F to have the norm-1 property have been provided. Moreover it was proved that in
Ju l 2 01 3 Uniform continuity of POVMs
Recently a characterization of uniformly continuous POVMs and a necessary condition for a uniformly continuous POVM F to have the norm-1 property have been provided. Moreover it was proved that in
A note on the relationship between localization and the norm-1 property
This paper focuses on the problem of localization in quantum mechanics. It is well known that it is not possible to define a localization observable for the photon by means of projection-valued

References

SHOWING 1-10 OF 42 REFERENCES
Convergence of probability measures
The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the
The norm-1-property of a quantum observable
A normalized positive operator measure $X\mapsto E(X)$ has the norm-1-property if $\no{E(X)}=1$ whenever $E(X)\ne O$. This property reflects the fact that the measurement outcome probabilities for
Measure Theory
These are some brief notes on measure theory, concentrating on Lebesgue measure on Rn. Some missing topics I would have liked to have included had time permitted are: the change of variable formula
Probability Theory and Related Fields. Manuscript-nr. Stochastic Invariant Imbedding Application to Stochastic Diierential Equations with Boundary Conditions
We study stochastic diierential equations of the type : dx t = f(t; x t)dt + d X k=1 k (t; x t) dw k t ; x 2 IR d ; t 2 0; T 0 ]: Instead of the customary initial value problem, where the initial
Probability Theory I
These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of
Characterizations of Commutative POV Measures
Two different characterizations of POV measures with commutative range are compared using a representation of some stochastic operators by (weak) Markov kernels. A representation by Choquet theorem
A note on the relationship between localization and the norm-1 property
This paper focuses on the problem of localization in quantum mechanics. It is well known that it is not possible to define a localization observable for the photon by means of projection-valued
Linear Operators
Linear AnalysisMeasure and Integral, Banach and Hilbert Space, Linear Integral Equations. By Prof. Adriaan Cornelis Zaanen. (Bibliotheca Mathematica: a Series of Monographs on Pure and Applied
Classical Representations of Quantum Mechanics Related to Statistically Complete Observables
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on
Fundamentals of the Theory of Operator Algebras
Comparison theory of projections--exercises and solutions Normal states and unitary equivalence of von Neumann algebras--exercises and solutions The trace--exercises and solutions Algebra and
...
1
2
3
4
5
...