Embeddings of operator ideals into<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="script">L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>-spaces on finite von Neumann algebras

Junge, Marius; Sukochev, Fedor; Zanin, Dmitriy

doi:10.1016/j.aim.2017.03.031

Cited by 12 publications

(4 citation statements)

References 45 publications

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“…We refer [18], [31], [14], [44], [13], [13] . We refer [16], [17], [18], [15], [43], [19], [37], [11], [20] and references therein for more information in this direction of research. Therefore, in view of the results appearing in [26], [27], [28], [29], [30], it is natural to study non-commutative analogs.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On Isometric Embeddability of $S_q^m$ into $S_p^n$ as non-commutative Quasi-Banach spaces

Chattopadhyay¹,

Hong²,

Pradhan³

et al. 2022

Preprint

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The existence of isometric embedding of S m q into S n p , where 1 ≤ p = q ≤ ∞ and m, n ≥ 2 has been recently studied in [6]. In this article, we extend the study of isometric embeddability beyond the above mentioned range of p and q. More precisely, we show that there is no isometric embedding of the commutative quasi-Banach space ℓ m q (R) into ℓ n p (R), where (q, p) ∈ (0, ∞) × (0, 1) and p = q. As non-commutative quasi-Banach spaces, we show that there is no isometric embedding of S m q into S n p , where (q, p) ∈ (0, 2) × (0, 1) ∪ {1} × (0, 1) \ { 1 n : n ∈ N} ∪ {∞} × (0, 1) \ { 1 n : n ∈ N} and p = q. Moreover, in some restrictive cases, we also show that there is no isometric embedding of S m q into S n p , where (q, p) ∈ [2, ∞) × (0, 1). To achieve our goal we significantly use Kato-Rellich theorem and multiple operator integrals in perturbation theory, followed by intricate computations involving power-series analysis.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

On Isometric Embeddability of $S_q^m$ into $S_p^n$ as non-commutative Quasi-Banach spaces

Chattopadhyay¹,

Hong²,

Pradhan³

et al. 2022

Preprint

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“…q-concave) function on the interval [0, 1] if and only if (2.7) (resp. (2.8)) holds for all 0 < t ≤ 1 and 0 < s ≤ 1 (see also [7,Lemma 6] and [24,Lemma 11]). This is equivalent to the p-convexity (resp.…”

Section: Remark 24 For Arbitrary Hilbert Space H and Every Positive I...mentioning

confidence: 96%

Lack of isomorphic embeddings of symmetric function spaces into operator ideals

Astashkin,

Huang,

Sukochev

2020

Preprint

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“…Then [9, Theorem 5.1] gives no information. However, by [31,Lemma 8] it is not hard to see that Φ is 2-convex and (2 + q)-concave, and hence the corresponding Burkholder-Gundy inequality holds due to Theorem 7.2 (ii). (ii) Suppose that p + q = 2.…”

Section: Noncommutative Martingale Inequalities: the φ-Moment Casementioning

confidence: 99%

Johnson-Schechtman inequalities for noncommutative martingales

Jiao¹,

Sukochev²,

Zanin³

et al. 2016

Preprint

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In this paper we study Johnson-Schechtman inequalities for noncommutative martingales. More precisely, disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space E(M) of a finite von Neumann algebra M without making any assumption on the Boyd indices of E. We show that we can obtain Johnson-Schechtman inequalities for arbitrary martingale difference sequences and that, in contrast with the classical case of independent random variables or the noncommutative case of freely independent random variables, the inequalities are one-sided except when E = L 2 (0, 1). As an application, we partly resolve a problem stated by Randrianantoanina and Wu in [48]. We also show that we can obtain sharp Φ-moment analogues for Orlicz functions satisfying p-convexity and q-concavity for 1 ≤ p ≤ 2, q = 2 and p = 2, 2 < q < ∞. This is new even for the classical case. We also extend and strengthen the noncommutative Burkholder-Gundy inequalities in symmetric spaces and in the Φ-moment case.

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Embeddings of operator ideals intoLp-spaces on finite von Neumann algebras

Abstract: Let L(H) be the * -algebra of all bounded operators on an infinite dimensional Hilbert space H and let (

Cited by 12 publications

References 45 publications

On Isometric Embeddability of $S_q^m$ into $S_p^n$ as non-commutative Quasi-Banach spaces

On Isometric Embeddability of $S_q^m$ into $S_p^n$ as non-commutative Quasi-Banach spaces

Lack of isomorphic embeddings of symmetric function spaces into operator ideals

Johnson-Schechtman inequalities for noncommutative martingales

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