| 1. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Completely bounded bimodule maps and spectral synthesis
- 2017
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 28:10
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Tidskriftsartikel (refereegranskat)abstract
- We initiate the study of the completely bounded multipliers of the Haagerup tensor product A(G) circle times(h) A(G) of two copies of the Fourier algebra A(G) of a locally compact group G. If E is a closed subset of G we let E# = {(s, t) : st. E} and show that if E# is a set of spectral synthesis for A(G) circle times(h) A(G) then E is a set of local spectral synthesis for A(G). Conversely, we prove that if E is a set of spectral synthesis for A(G) and G is a Moore group then E# is a set of spectral synthesis for A(G)circle times(h) A(G). Using the natural identification of the space of all completely bounded weak* continuous VN(G)' bimodule maps with the dual of A(G)circle times(h) A(G), we show that, in the case G is weakly amenable, such a map leaves the multiplication algebra of L-infinity(G) invariant if and only if its support is contained in the antidiagonal of G.
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| 2. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Completely bounded maps and invariant subspaces
- 2020
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 294:1-2, s. 471-489
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Albeverio, Sergio, et al.
(författare)
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On *-representations of a deformation of a Wick analogue of the CAR algebra
- 2005
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Ingår i: Reports on Mathematical Physics. - 0034-4877. ; 56:2, s. 175-196-196
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Tidskriftsartikel (refereegranskat)abstract
- The classification of irreducible *-representations of deformations of canonical anti-commutation relations is given. A description of the corresponding enveloping C*-algebra is presented in terms of continuous matrix-functions satisfying certain boundary conditions.
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| 4. |
- Brannan, Michael, et al.
(författare)
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Quantum no-signalling bicorrelations
- 2024
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Ingår i: Advances in Mathematics. - 1090-2082 .- 0001-8708. ; 449
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Tidskriftsartikel (refereegranskat)abstract
- We introduce classical and quantum no-signalling bicorrelations and characterise the different types thereof in terms of states on operator system tensor products, exhibiting connections with bistochastic operator matrices and with dilations of quantum magic squares. We define concurrent bicorrelations as a quantum input-output generalisation of bisynchronous correlations. We show that concurrent bicorrelations of quantum commuting type correspond to tracial states on the universal C*-algebra of the projective free unitary quantum group, showing that in the quantum input-output setup, quantum permutations of finite sets must be replaced by quantum automorphisms of matrix algebras. We apply our results to study the quantum graph isomorphism game, describing the game C*-algebra in this case, and make precise connections with the algebraic notions of quantum graph isomorphism, existing presently in the literature.
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| 5. |
- Brannan, Michael, et al.
(författare)
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Synchronicity for quantum non-local games
- 2023
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 284:2
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Tidskriftsartikel (refereegranskat)abstract
- We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes. We define *-algebras and C*-algebras of concurrent classical-to-quantum and concurrent quantum non-local games, and algebraic versions of the orthogonal rank of a graph. We show that quantum homomorphisms of quantum graphs can be viewed as entanglement assisted classical homomorphisms of the graphs, and give descriptions of the perfect quantum commuting and the perfect approximately quantum strategies for the quantum graph homomorphism game. We specialise the latter results to the case where the inputs of the game are based on a classical graph.
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| 6. |
- Helgason, Sigurdur, et al.
(författare)
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Letters to the editor
- 2021
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Ingår i: Notices of the American Mathematical Society. - Malmö : Malmö universitet. - 1088-9477 .- 0002-9920. ; 68:9, s. 1453-1454:2, s. i-iii
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 7. |
- Kuzmin, Olexiy, 1995, et al.
(författare)
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Classification of irrational Θ-deformed CAR C*-algebras
- 2021
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Ingår i: Münster Journal of Mathematics. - 1867-5786 .- 1867-5778. ; 14:11, s. 559-583
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Tidskriftsartikel (refereegranskat)abstract
- Given a skew-symmetric matrix Θ we consider the universal enveloping C*-algebra CARΘ of the ∗-algebra generated by a_1,…,a_n subject to relations a_i*a_i+a_ia_i*=1, a_i*a_j=e^{2πiΘij}a_ja_i*, a_ia_j=e^{−2πiΘij}a_ja_i. We prove that CARΘ has a C(Kn)-structure, where Kn=[0,1/2]^n is the hypercube and describe the fibers. We classify irreducible representations of CARΘ in terms of representations of higher-dimensional noncommutative tori. We prove that for a given irrational Θ1 there are only finitely many Θ2 such that CARΘ1≃CARΘ2. Namely, CARΘ1≃CARΘ2 implies (Θ1)ij=±(Θ2)σ(i,j)modZ for a bijection σ of the set {(i,j):i
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| 8. |
- Le Merdy, Christian, et al.
(författare)
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Bilinear operator multipliers into the trace class
- 2020
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 279:7
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Tidskriftsartikel (refereegranskat)abstract
- Given Hilbert spaces H1,H2,H3, we consider bilinear maps defined on the cartesian product S2(H2,H3)×S2(H1,H2) of spaces of Hilbert-Schmidt operators and valued in either the space B(H1,H3) of bounded operators, or in the space S1(H1,H3) of trace class operators. We introduce modular properties of such maps with respect to the commutants of von Neumann algebras Mi⊂B(Hi), i=1,2,3, as well as an appropriate notion of complete boundedness for such maps. We characterize completely bounded module maps u:S2(H2,H3)×S2(H1,H2)→B(H1,H3) by the membership of a natural symbol of u to the von Neumann algebra tensor product M1⊗‾M2op⊗‾M3. In the case when M2 is injective, we characterize completely bounded module maps u:S2(H2,H3)×S2(H1,H2)→S1(H1,H3) by a weak factorization property, which extends to the bilinear setting a famous description of bimodule linear mappings going back to Haagerup, Effros-Kishimoto, Smith and Blecher-Smith. We make crucial use of a theorem of Sinclair-Smith on completely bounded bilinear maps valued in an injective von Neumann algebra, and provide a new proof of it, based on Hilbert C⁎-modules.
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| 9. |
- Levene, Rupert, et al.
(författare)
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Schur multipliers of Cartan pairs
- 2017
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Ingår i: Proceedings of the Edinburgh Mathematical Society. - 1464-3839 .- 0013-0915. ; 60:2, s. 413-440
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Tidskriftsartikel (refereegranskat)abstract
- We define the Schur multipliers of a separable von Neumann algebra M with Cartan maximal abelian self-adjoint algebra A, generalizing the classical Schur multipliers of B(2). We characterize these as the normal A-bimodule maps on M. If M contains a direct summand isomorphic to the hyperfinite II 1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product A⊗ehA are strictly contained in the algebra of all Schur multipliers.
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| 10. |
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