Completely Bounded and Ideal Norms of Multiplication Operators and Schur Multipliers

Oikhberg, Timur

doi:10.1007/s00020-010-1751-5

Integr. Equ. Oper. Theory

2010

DOI: 10.1007/s00020-010-1751-5

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Completely Bounded and Ideal Norms of Multiplication Operators and Schur Multipliers

Timur Oikhberg

Abstract: We estimate the completely bounded norms, the completely p-nuclear norms, and the completely p-summing norms of certain multiplication operators and Schur multipliers. Mathematics Subject Classification (2010).Primary: 46L07; Secondary: 47B10, 47B49, 47L20.

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Cited by 3 publications

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“…Remark 5.6 from [31] then suggests how we can separate the values ω * (G) and V (G). Using [42], we can find matrices ϕ and ψ for which |ϕ ij | ≤ |ψ ij | for all i, j, but ϕ 1 ≫ ψ 1 .…”

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Rank-one quantum games

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Abstract. In this work we study rank-one quantum games. In particular, we focus on the study of the computability of the entangled value ω * and the entangled value with one-way quantum communication ω qow of these games. We will show that the value ω * can be efficiently approximated up to a 4-multiplicative factor and that ω qow can be efficiently computed. We also study the behavior of these values under the parallel repetition of rank-one quantum games. We will show that ω * does not verify a perfect parallel repetition theorem and that ω qow does verify such a theorem.

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Rank-one quantum games

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Operator p-compact mappings

Chávez-Domínguez

Dimant

Galicer

2019

Journal of Functional Analysis

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Complemented subspaces of spaces of multilinear forms and tensor products, II. Noncommutative Lp spaces

Sánchez¹

2015

Journal of Mathematical Analysis and Applications

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+ q −1 = 1, then the space of multilinear forms B(S p1 , . . . , S pk ; C) contains a complemented subspace isometric to S q . We construct explicit embeddings of S n r into S n p ⊗ S n q for r −1 = p −1 + q −1 whose range is complemented by a "natural" norm-one projection. As a byproduct we compute the nuclear norm of some multiplication operators: if r −1 + 1 = p −1 + q −1 , with p, q ≥ 1, then, given an n-by-n matrix φ, the nuclear norm of the multiplication operator h ∈ S n p → h · φ ∈ S n q is n times the norm of φ in S n r , where r = max(1, r). A number of results on general noncommutative L p spaces are also included.

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Completely Bounded and Ideal Norms of Multiplication Operators and Schur Multipliers

Abstract: We estimate the completely bounded norms, the completely p-nuclear norms, and the completely p-summing norms of certain multiplication operators and Schur multipliers. Mathematics Subject Classification (2010).Primary: 46L07; Secondary: 47B10, 47B49, 47L20.

Cited by 3 publications

References 21 publications

Rank-one quantum games

Rank-one quantum games

Operator p-compact mappings

Complemented subspaces of spaces of multilinear forms and tensor products, II. Noncommutative Lp spaces

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