The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Rajai Nasser - One of the best experts on this subject based on the ideXlab platform.
-
Topological Structures on DMC Spaces
Entropy, 2018Co-Authors: Rajai NasserAbstract:Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean Topology by the equivalence relation. A Topology on the space of equivalent channels with fixed input alphabet X and arbitrary but finite output alphabet is said to be natural if and only if it induces the quotient Topology on the subspaces of equivalent channels sharing the same output alphabet. We show that every natural Topology is σ -compact, separable and path-connected. The finest natural Topology, which we call the Strong Topology, is shown to be compactly generated, sequential and T 4 . On the other hand, the Strong Topology is not first-countable anywhere, hence it is not metrizable. We introduce a metric distance on the space of equivalent channels which compares the noise levels between channels. The induced metric Topology, which we call the noisiness Topology, is shown to be natural. We also study topologies that are inherited from the space of meta-probability measures by identifying channels with their Blackwell measures.
-
ISIT - Topological structures on DMC spaces
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: Rajai NasserAbstract:Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean Topology by the equivalence relation. We show that this Topology is compact, path-connected and metrizable. A Topology on the space of equivalent channels with fixed input alphabet X and arbitrary but finite output alphabet is said to be natural if and only if it induces the quotient Topology on the subspaces of equivalent channels sharing the same output alphabet. We show that every natural Topology is σ-compact, separable and path-connected. On the other hand, if |X| ≥ 2, a Hausdorff natural Topology is not Baire and it is not locally compact anywhere. This implies that no natural Topology can be completely metrized if |X| ≥ 2. The finest natural Topology, which we call the Strong Topology, is shown to be compactly generated, sequential and T 4 . On the other hand, the Strong Topology is not first-countable anywhere, hence it is not metrizable. We show that in the Strong Topology, a subspace is compact if and only if it is rank-bounded and Strongly-closed. We provide a necessary and sufficient condition for a sequence of channels to converge in the Strong Topology. We introduce a metric distance on the space of equivalent channels which compares the noise levels between channels. The induced metric Topology, which we call the noisiness Topology, is shown to be natural. We also study topologies that are inherited from the space of meta-probability measures by identifying channels with their Blackwell measures. We show that the weak-∗ Topology is exactly the same as the noisiness Topology and hence it is natural. We prove that if |X| ≥ 2, the total variation Topology is not natural nor Baire, hence it is not completely metrizable. Moreover, it is not locally compact anywhere. Finally, we show that the Borel σ-algebra is the same for all Hausdorff natural topologies.
-
A Characterization of the Shannon Ordering of Communication Channels
arXiv: Information Theory, 2017Co-Authors: Rajai NasserAbstract:The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that $W'$ contains $W$ if and only if $W$ is the skew-composition of $W'$ with a convex-product channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two channels are said to be Shannon-equivalent if each one is contained in the other. We investigate the topologies that can be constructed on the space of Shannon-equivalent channels. We introduce the Strong Topology and the BRM metric on this space. Finally, we study the continuity of a few channel parameters and operations under the Strong Topology.
-
ISIT - A characterization of the Shannon ordering of communication channels
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: Rajai NasserAbstract:The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that W' contains W if and only if W is the skew-composition of W' with a convex-product channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two channels are said to be Shannon-equivalent if each one is contained in the other. We investigate the topologies that can be constructed on the space of Shannon-equivalent channels. We introduce the Strong Topology and the BRM metric on this space. Finally, we study the continuity of a few channel parameters and operations under the Strong Topology.
Antonio M. Peralta - One of the best experts on this subject based on the ideXlab platform.
-
measures of weak non compactness in preduals of von neumann algebras and jbw triples
Journal of Functional Analysis, 2020Co-Authors: Jan Hamhalter, Antonio M. Peralta, Ondřej F K Kalenda, Hermann PfitznerAbstract:Abstract We prove, among other results, that three standard measures of weak non-compactness coincide in preduals of JBW⁎-triples. This result is new even for preduals of von Neumann algebras. We further provide a characterization of JBW⁎-triples with Strongly WCG predual and describe the order of seminorms defining the Strong⁎ Topology. As a byproduct we improve a characterization of weakly compact subsets of a JBW⁎-triple predual, providing so a proof for a conjecture, open for almost eighteen years, on weakly compact operators from a JB⁎-triple into a complex Banach space.
-
Weakly compact operators and the Strong ∗ Topology for a Banach space
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2010Co-Authors: Antonio M. Peralta, Ignacio Villanueva, J. D. Maitland Wright, Kari YlinenAbstract:The Strong* Topology s_(X) of a Banach space X is defined as the locally convex Topology generated by the seminorms x 7! kSxk for bounded linear maps S from X into Hilbert spaces. The w-right Topology for X, _(X), is a Stronger locally convex Topology, which may be analogously characterised by taking reflexive Banach spaces in place of Hilbert spaces. For any Banach space Y , a linear map T : X ! Y is known to be weakly compact precisely when T is continuous from the w-right Topology to the norm Topology of Y . The main results deal with conditions for, and consequences of, the coincidence of these two topologies on norm bounded sets. A large class of Banach spaces, including all C_-algebras, and more generally, all JB_-triples, exhibit this behaviour.
-
weakly compact operators and the Strong Topology for a banach space
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2010Co-Authors: Antonio M. Peralta, Ignacio Villanueva, J Maitland D Wright, Kari YlinenAbstract:The Strong* Topology s_(X) of a Banach space X is defined as the locally convex Topology generated by the seminorms x 7! kSxk for bounded linear maps S from X into Hilbert spaces. The w-right Topology for X, _(X), is a Stronger locally convex Topology, which may be analogously characterised by taking reflexive Banach spaces in place of Hilbert spaces. For any Banach space Y , a linear map T : X ! Y is known to be weakly compact precisely when T is continuous from the w-right Topology to the norm Topology of Y . The main results deal with conditions for, and consequences of, the coincidence of these two topologies on norm bounded sets. A large class of Banach spaces, including all C_-algebras, and more generally, all JB_-triples, exhibit this behaviour.
Hermann Pfitzner - One of the best experts on this subject based on the ideXlab platform.
-
measures of weak non compactness in preduals of von neumann algebras and jbw triples
Journal of Functional Analysis, 2020Co-Authors: Jan Hamhalter, Antonio M. Peralta, Ondřej F K Kalenda, Hermann PfitznerAbstract:Abstract We prove, among other results, that three standard measures of weak non-compactness coincide in preduals of JBW⁎-triples. This result is new even for preduals of von Neumann algebras. We further provide a characterization of JBW⁎-triples with Strongly WCG predual and describe the order of seminorms defining the Strong⁎ Topology. As a byproduct we improve a characterization of weakly compact subsets of a JBW⁎-triple predual, providing so a proof for a conjecture, open for almost eighteen years, on weakly compact operators from a JB⁎-triple into a complex Banach space.
Agissilaos Athanassoulis - One of the best experts on this subject based on the ideXlab platform.
-
Strong phase-space semiclassical asymptotics
SIAM Journal on Mathematical Analysis, 2011Co-Authors: Agissilaos Athanassoulis, Thierry PaulAbstract:Wigner and Husimi transforms have long been used for the phase-space reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are concerned with semiclassical limits in the Strong Topology, i.e. approximation of Wigner functions by solutions of the Liouville equation in $L^2$ and Sobolev norms. The results obtained improve the state of the art, and highlight the role of potential regularity, especially through the regularity of the Wigner equation. It must be mentioned that the Strong convergence can be shown up to $O(log \frac{1}\epsilon)$ time-scales, which is well known to be, in general, the limit of validity of semiclassical asymptotics.
-
Strong phase-space semiclassical asymptotics
SIAM Journal on Mathematical Analysis, 2011Co-Authors: Thierry Paul, Agissilaos AthanassoulisAbstract:Wigner and Husimi transforms have long been used for the phase- space reformulation of SchrÄodinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are con- cerned with semiclassical limits in the Strong Topology, i.e. approxima- tion of Wigner functions by solutions of the Liouville equation in L2 and Sobolev norms. The results obtained improve the state of the art, and highlight the role of potential regularity, especially through the regularity of the Wigner equation. It must be mentioned that the Strong conver- gence can be shown up to logarithmic time-scales, which is well known to be, in general, the limit of validity of semiclassical asymptotics.
Thierry Paul - One of the best experts on this subject based on the ideXlab platform.
-
Strong phase-space semiclassical asymptotics
SIAM Journal on Mathematical Analysis, 2011Co-Authors: Agissilaos Athanassoulis, Thierry PaulAbstract:Wigner and Husimi transforms have long been used for the phase-space reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are concerned with semiclassical limits in the Strong Topology, i.e. approximation of Wigner functions by solutions of the Liouville equation in $L^2$ and Sobolev norms. The results obtained improve the state of the art, and highlight the role of potential regularity, especially through the regularity of the Wigner equation. It must be mentioned that the Strong convergence can be shown up to $O(log \frac{1}\epsilon)$ time-scales, which is well known to be, in general, the limit of validity of semiclassical asymptotics.
-
Strong phase-space semiclassical asymptotics
SIAM Journal on Mathematical Analysis, 2011Co-Authors: Thierry Paul, Agissilaos AthanassoulisAbstract:Wigner and Husimi transforms have long been used for the phase- space reformulation of SchrÄodinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are con- cerned with semiclassical limits in the Strong Topology, i.e. approxima- tion of Wigner functions by solutions of the Liouville equation in L2 and Sobolev norms. The results obtained improve the state of the art, and highlight the role of potential regularity, especially through the regularity of the Wigner equation. It must be mentioned that the Strong conver- gence can be shown up to logarithmic time-scales, which is well known to be, in general, the limit of validity of semiclassical asymptotics.
