Schur products and matrix completions

Paulsen, Vern I.; Power, S. C.; Smith, Roger

doi:10.1016/0022-1236(89)90050-5

Cited by 106 publications

(86 citation statements)

References 7 publications

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“…However, it is simpler to prove Theorem 3.1 directly. Theorem 3.1(a) is due to Haagerup (unpublished); it was proved, in a more general form (involving partial matrices), in [13,Theorem 3.2]; it was also derived by Ando and Okubo, using the identity above, from the main result in [2], which is Theorem 3.2(a). All these proofs are based on Arvenson's Extension Theorem for positive maps on C* algebras.…”

Section: Hadamard Productsmentioning

confidence: 97%

Matrix completions, norms and Hadamard products

Mathias¹

1993

Proc. Amer. Math. Soc.

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Abstract.Let Mm ," (respectively, H") denote the space of mxn complex matrices (respectively, n x n Hermitian matrices). Let S C H" be a closed convex set. We obtain necessary and sufficient conditions for X0 £ S to attain the maximum in the following concave maximization problem: We also consider other norms that can be represented in this way and show that if a norm can be represented in this way then so can its dual.

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Section: Hadamard Productsmentioning

confidence: 97%

Matrix completions, norms and Hadamard products

Mathias¹

1993

Proc. Amer. Math. Soc.

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“…If S a·b acts on X = B( 2 ), one can prove the above lemma by using the version of Stinespring's Extension Theorem for restricted Schur multipliers developed in [19]. However, the above proof has the advantages of being constructive and of working for arbitrary unconditional matrix spaces.…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

Restricted Schur multipliers and their applications

Oikhberg

2010

Proc. Amer. Math. Soc.

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“…We may assume D = 1. Let R ′ × C ′ be any finite subset of R × C. By [16,Th. 3.2], there exist vectors w c and v r of norm at most 1 in a Hilbert space H such that ϕ rc = w c , v r for every (r, c)…”

Section: Relative Schur Multipliersmentioning

confidence: 99%

“…If (a) holds, every sequence of signs ǫ ∈ {−1, 1} I is a Schur multiplier on S ∞ I . By a convexity argument, this implies that every bounded sequence is a Schur multiplier on S ∞ I , which may be extended to a Schur multiplier on S ∞ with the same norm by [16,Cor. 3.3].…”

Section: Sketch Of Proof (A) ⇒ (B)mentioning

confidence: 99%

Cycles and 1-Unconditional Matrices

Neuwirth¹

2006

Proc. Lond. Math. Soc.

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We characterize the 1-unconditional subsets (erc) (r,c)∈I of the set of elementary matrices in the Schatten-von-Neumann class S p . The set of couples I must be the set of edges of a bipartite graph without cycles of even length 4 l p if p is an even integer, and without cycles at all if p is a positive real number that is not an even integer. In the latter case, I is even a Varopoulos set of V -interpolation of constant 1. We also study the metric unconditional approximation property for the space S p I spanned by (erc) (r,c)∈I in S p .

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Schur products and matrix completions

Cited by 106 publications

References 7 publications

Matrix completions, norms and Hadamard products

Matrix completions, norms and Hadamard products

Restricted Schur multipliers and their applications

Cycles and 1-Unconditional Matrices

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