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A Hausdorff topological group G is minimal if every continuous isomorphism f:G→H between G and a Hausdorff topological group H is open. Significantly strengthening a 1981 result of Stoyanov, we prove the following theorem: For every infinite minimal abelian group G there exists a sequence of cardinals such that
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Let A1,…,AN be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle
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Ping-Bao Liao 《Linear algebra and its applications》2009,430(4):1236-197
Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f,d:R→A are linear maps satisfying that
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R. Balasubramanian D.J. Prabhakaran 《Journal of Mathematical Analysis and Applications》2007,336(1):542-555
For γ?0 and β<1 given, let Pγ(β) denote the class of all analytic functions f in the unit disk with the normalization f(0)=f′(0)−1=0 and satisfying the condition
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The higher Randi? index Rt(G) of a simple graph G is defined as
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Monica Ilie 《Journal of Functional Analysis》2004,213(1):88-110
Let G be a locally compact group and let B(G) be the dual space of C∗(G), the group C∗ algebra of G. The Fourier algebra A(G) is the closed ideal of B(G) generated by elements with compact support. The Fourier algebras have a natural operator space structure as preduals of von Neumann algebras. Given a completely bounded algebra homomorphism we show that it can be described, in terms of a piecewise affine map with Y in the coset ring of H, as follows
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Raimundas Vidūnas 《Linear algebra and its applications》2007,422(1):39-57
Let V denote a vector space with finite positive dimension, and let (A, A∗) denote a Leonard pair on V. As is known, the linear transformations A, A∗ satisfy the Askey-Wilson relations
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Christian Le Merdy 《Advances in Mathematics》2010,224(4):1641-2998
Let G be an amenable group, let X be a Banach space and let π:G→B(X) be a bounded representation. We show that if the set is γ-bounded then π extends to a bounded homomorphism w:C∗(G)→B(X) on the group C∗-algebra of G. Moreover w is necessarily γ-bounded. This extends to the Banach space setting a theorem of Day and Dixmier saying that any bounded representation of an amenable group on Hilbert space is unitarizable. We obtain additional results and complements when G=Z, R or T, and/or when X has property (α). 相似文献
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Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
Chi-Kwong Li 《Linear algebra and its applications》2009,430(7):1739-1398
Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form
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R. Nair 《Indagationes Mathematicae》2003,14(2):233-240
Let a = (aii=1∞ be a strictly increasing sequence of natural numbers and let be a space of Lebesgue measurable functions defined on [0,1). Let <y> denote the fractional part of the real number y. We say that a is an ∗ sequence if for each f ?
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Eun-Young Lee 《Linear algebra and its applications》2011,435(4):735-741
Let f(t) be a non-negative concave function on the positive half-line. Given an arbitrary partitioned positive semi-definite matrix, we show that
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Chao ChenLitan Yan 《Statistics & probability letters》2011,81(8):1003-1012
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Measures of weak noncompactness are formulae that quantify different characterizations of weak compactness in Banach spaces: we deal here with De Blasi's measure ω and the measure of double limits γ inspired by Grothendieck's characterization of weak compactness. Moreover for bounded sets H of a Banach space E we consider the worst distance k(H) of the weak∗-closure in the bidual of H to E and the worst distance ck(H) of the sets of weak∗-cluster points in the bidual of sequences in H to E. We prove the inequalities
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Aljoša Peperko 《Linear algebra and its applications》2011,435(4):902-907
Given a bounded set Ψ of n×n non-negative matrices, let ρ(Ψ) and μ(Ψ) denote the generalized spectral radius of Ψ and its max version, respectively. We show that
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Ana Cecilia de la Maza 《Journal of Number Theory》2008,128(8):2199-2213
Given a number field K and a subgroup G⊂K∗ of the multiplicative group of K, Silverman defined the G-height H(θ;G) of an algebraic number θ as