The Experts below are selected from a list of 96 Experts worldwide ranked by ideXlab platform
Amílcar Sernadas - One of the best experts on this subject based on the ideXlab platform.
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Preservation of Craig interpolation
2020Co-Authors: Cristina Sernadas, João Rasga, Amílcar SernadasAbstract:The Product of Matrix logics, possibly with additional interaction axioms, is shown to preserve a slightly relaxed notion of Craig interpolation. The result is established symbolically, capitalizing on the complete axiomatization of the Product of Matrix logics provided by their meet-combination. Along the way preservation of the metatheorem of deduction is also proved. The computation of the interpolant in the resulting logic is proved to be polynomially reducible to the computation of the interpolants in the two given logics. Illustrations are provided for classical, intuitionistic and modal propositional logics.
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Preservation of Craig interpolation by the Product of Matrix logics
Journal of Applied Logic, 2013Co-Authors: Cristina Sernadas, João Rasga, Amílcar SernadasAbstract:Abstract The Product of Matrix logics, possibly with additional interaction axioms, is shown to preserve a slightly relaxed notion of Craig interpolation. The result is established symbolically, capitalizing on the complete axiomatization of the Product of Matrix logics provided by their meet-combination. Along the way preservation of the metatheorem of deduction is also proved. The computation of the interpolant in the resulting logic is proved to be polynomially reducible to the computation of the interpolants in the two given logics. Illustrations are provided for classical, intuitionistic and modal propositional logics.
Mikael Rørdam - One of the best experts on this subject based on the ideXlab platform.
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Factorizable Maps and Traces on the Universal Free Product of Matrix Algebras
International Mathematics Research Notices, 2019Co-Authors: Magdalena Musat, Mikael RørdamAbstract:Abstract We relate factorizable quantum channels on $M_n({\mathbb{C}})$, for $n \ge 2$, via their Choi Matrix, to certain matrices of correlations, which, in turn, are shown to be parametrized by traces on the unital free Product $M_n({\mathbb{C}}) \ast _{\mathbb{C}} M_n({\mathbb{C}})$. Factorizable maps with a finite dimensional ancilla are parametrized by finite dimensional traces on $M_n({\mathbb{C}}) \ast _{\mathbb{C}} M_n({\mathbb{C}})$, and factorizable maps that approximately factor through finite dimensional $C^\ast $-algebras are parametrized by traces in the closure of the finite dimensional ones. The latter set of traces is shown to be equal to the set of hyperlinear traces on $M_n({\mathbb{C}}) \ast _{\mathbb{C}} M_n({\mathbb{C}})$. We finally show that each metrizable Choquet simplex is a face of the simplex of tracial states on $M_n({\mathbb{C}}) \ast _{\mathbb{C}} M_n({\mathbb{C}})$.
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Factorizable maps and traces on the universal free Product of Matrix algebras.
arXiv: Operator Algebras, 2019Co-Authors: Magdalena Musat, Mikael RørdamAbstract:We relate factorizable quantum channels on $M_n$, for $n \ge 2$, via their Choi Matrix, to certain correlation matrices, which, in turn, are shown to be parametrized by traces on the unital free Product $M_n * M_n$. Factorizable maps that admit a finite dimensional ancilla are parametrized by finite dimensional traces on $M_n * M_n$, and factorizable maps that approximately factor through finite dimensional C*-algebras are parametrized by traces in the closure of the finite dimensional ones. The latter set is shown to be equal to the set of hyperlinear traces on $M_n * M_n$. We finally show that each metrizable Choquet simplex is a face of the simplex of tracial states on $M_n * M_n$.
Dmitry S. Kalyuzhny Uı-verbovetzki Uı - One of the best experts on this subject based on the ideXlab platform.
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On the {Bessmertny\u{\i}} Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes
arXiv: Functional Analysis, 2004Co-Authors: Dmitry S. Kalyuzhny Uı-verbovetzki UıAbstract:We generalize our earlier results from \cite{K} on the Bessmertny\ui class of operator-valued functions holomorphic in the open right poly-halfplane which admit representation as a Schur complement of a block of a linear homogeneous operator-valued function with positive semidefinite operator coefficients, to the case of a Product of open right Matrix halfplanes. Several equivalent characterizations of this generalized Bessmertny\ui class are presented. In particular, its intimate connection with the Agler--Schur class of holomorphic contractive operator-valued functions on the Product of Matrix unit disks is established.
Dmitry S. Kalyuzhnyĭ-verbovetzkiĭ - One of the best experts on this subject based on the ideXlab platform.
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On the Bessmertnyĭ Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes
arXiv: Functional Analysis, 2020Co-Authors: Dmitry S. Kalyuzhnyĭ-verbovetzkiĭAbstract:We generalize our earlier results from [9] on the Bessmertnyĭ class of operator-valued functions holomorphic in the open right poly-halfplane which admit representation as a Schur complement of a block of a linear homogeneous operator-valued function with positive semidefinite operator coefficients, to the case of a Product of open right Matrix halfplanes. Several equivalent characterizations of this generalized Bessmertnyĭ class are presented. In particular, its intimate connection with the Agler-Schur class of holomorphic contractive operator-valued functions on the Product of Matrix unit disks is established.
Cristina Sernadas - One of the best experts on this subject based on the ideXlab platform.
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Preservation of Craig interpolation
2020Co-Authors: Cristina Sernadas, João Rasga, Amílcar SernadasAbstract:The Product of Matrix logics, possibly with additional interaction axioms, is shown to preserve a slightly relaxed notion of Craig interpolation. The result is established symbolically, capitalizing on the complete axiomatization of the Product of Matrix logics provided by their meet-combination. Along the way preservation of the metatheorem of deduction is also proved. The computation of the interpolant in the resulting logic is proved to be polynomially reducible to the computation of the interpolants in the two given logics. Illustrations are provided for classical, intuitionistic and modal propositional logics.
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Preservation of Craig interpolation by the Product of Matrix logics
Journal of Applied Logic, 2013Co-Authors: Cristina Sernadas, João Rasga, Amílcar SernadasAbstract:Abstract The Product of Matrix logics, possibly with additional interaction axioms, is shown to preserve a slightly relaxed notion of Craig interpolation. The result is established symbolically, capitalizing on the complete axiomatization of the Product of Matrix logics provided by their meet-combination. Along the way preservation of the metatheorem of deduction is also proved. The computation of the interpolant in the resulting logic is proved to be polynomially reducible to the computation of the interpolants in the two given logics. Illustrations are provided for classical, intuitionistic and modal propositional logics.