Algebraic tensor products and internal homs of noncommutative L -spaces

Pavlov, Dmitri

doi:10.1016/j.jmaa.2016.11.060

Cited by 3 publications

(1 citation statement)

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“…To return to the motivating discussion, we recall briefly the framework relevant to [24]. That paper works extensively with what it calls I-graded von Neumann algebras, where…”

Section: (Non-)presentabilitymentioning

confidence: 99%

Monadic forgetful functors and (non-)presentability for $C^$- and $W^$-algebras

Chirvăsitu¹,

Ko²

2022

Preprint

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We prove that the forgetful functors from the categories of C * -and W * -algebras to Banach * -algebras, Banach algebras or Banach spaces are all monadic, answering a question of J.Rosický, and that the categories of unital (commutative) C * -algebras are not locally-isometry ℵ 0 -generated either as plain or as metric-enriched categories, answering a question of I. Di Liberti and Rosický.We also prove a number of negative presentability results for the category of von Neumann algebras: not only is that category not locally presentable, but in fact its only presentable objects are the two algebras of dimension ≤ 2. For the same reason, for a locally compact abelian group G the category of G-graded von Neumann algebras is not locally presentable.

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“…To return to the motivating discussion, we recall briefly the framework relevant to [24]. That paper works extensively with what it calls I-graded von Neumann algebras, where…”

Section: (Non-)presentabilitymentioning

confidence: 99%

Monadic forgetful functors and (non-)presentability for $C^$- and $W^$-algebras

Chirvăsitu¹,

Ko²

2022

Preprint

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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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