共查询到20条相似文献,搜索用时 15 毫秒
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We study the structure of nilpotent completely positive maps in terms of Choi-Kraus coefficients. We prove several inequalities, including certain majorization type inequalities for dimensions of kernels of powers of nilpotent completely positive maps. 相似文献
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Sze-kai Tsui 《Proceedings of the American Mathematical Society》1996,124(2):437-445
Let be unital -algebras and be the set of all completely positive linear maps of into . In this article we characterize the extreme elements in , for all , and pure elements in in terms of a self-dual Hilbert module structure induced by each in . Let be the subset of consisting of -module maps for a von Neumann algebra . We characterize normal elements in to be extreme. Results here generalize various earlier results by Choi, Paschke and Lin.
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We investigate certain classes of normal completely positive (CP) maps on the hyperfinite II1 factorA. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such
CP maps.
Dedicated to Professor K B Sinha 相似文献
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Sehie Park 《Proceedings of the American Mathematical Society》1996,124(10):3109-3114
We present a simple proof of the Leray-Schauder type theorem for approximable multimaps given recently by Ben-El-Mechaiekh and Idzik. We apply this theorem to obtain a Schaefer type theorem, the Birkhoff-Kellogg type theorems, a Penot type theorem for non-self-maps, and quasi-variational inequalities, all related to compact closed approximable maps.
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Julio C. García 《Mathematical Notes》1999,65(2):159-167
The paper suggests a constructive characterization of unbounded completely positive maps introduced earlier by Chebotarev
for the theory of quantum dynamical semigroups. We prove that such cones are generated by a positive self-adjoint “reference”
operator ΛεB(H) as follows: for any completely positive unbounded map Ф(·)εCPn*(F) these exists a completely positive normal bounded mapR(·)εCPn(H) such that ϕ(·)=ΛR(·)Λ. The class contains mappings that are unclosable sesquilinear forms.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 194–205, February, 1999. 相似文献
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Juha-Pekka Pellonpää 《Positivity》2014,18(1):61-79
Convex sets of completely positive maps and positive-(semi)definite kernels are considered in a very general context of modules over $C^*$ -algebras and a complete characterization of their (regular) extremal points is obtained. As a byproduct, we determine extremal autocorrelation functions. We present a generalization for the Choi isomorphism widely used in quantum information theory and generalize the concept of a completely positive quantum instrument. 相似文献
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L. Gó rniewicz S. A. Marano M. Slosarski 《Proceedings of the American Mathematical Society》1996,124(9):2675-2683
For a class of contractive multivalued maps defined on a complete absolute retract and with closed bounded values, the set of fixed points is proved to be an absolute retract. This result unifies and extends to arbitrary absolute retracts both Theorem 1 by Ricceri [Atti Accad. Naz. Lincei Rend. Cl.Sci. Fis. Mat. Natur. (8) 81 (1987), 283--286] and Theorem 1 by Bressan, Cellina, and Fryszkowski [Proc. Amer. Math. Soc. 112 (1991), 413--418].
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V. V. Chistyakov 《Doklady Mathematics》2012,86(1):515-518
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We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive
map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we
study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007. 相似文献
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Bebe Prunaru 《Journal of Mathematical Analysis and Applications》2009,350(1):333-179
Let 1?n?∞, and let be a row contraction on some Hilbert space H. Let F(T) be the space of all X∈B(H) such that . We show that, if non-zero, this space is completely isometric to the commutant of the Cuntz part of the minimal isometric dilation of . 相似文献
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The Fock construction used by Davies in his theory of quantum stochastic processes yields a semigroup of completely positive maps on the C1-algebra of the CCR. We show how such semigroups may be constructed using an arbitrary representation of the CCR and we investigate some of their properties. 相似文献
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An operator convex function on (0,∞) which satisfies the symmetry condition k(x−1)=xk(x) can be used to define a type of non-commutative multiplication by a positive definite matrix (or its inverse) using the primitive concepts of left and right multiplication and the functional calculus. The operators for the inverse can be used to define quadratic forms associated with Riemannian metrics which contract under the action of completely positive trace-preserving maps. 相似文献
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Donal O'Regan 《Integral Equations and Operator Theory》1997,28(3):321-329
Several new fixed point results are presented for set valued maps. The maps we discuss are either ofM
* type or of regularly approximable type.47H10 相似文献