Pith Number

pith:R5OQV66T

pith:2026:R5OQV66TQU3OCOLEAIK3S23FRP

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Quantum Doubly Stochastic Operators on Non-commutative $L_p$-Spaces

Emma Sulaver

Positive trace-preserving maps define quantum doubly stochastic operators on non-commutative L_p-spaces.

arxiv:2605.17711 v1 · 2026-05-18 · math.OA · math.FA

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4 Citations open

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Claims

C1strongest claim

We introduce and systematically develop the theory of quantum doubly stochastic operators, i.e. positive, trace-preserving maps on non-commutative L_p-spaces associated to semifinite von Neumann algebras.

C2weakest assumption

That the non-commutative L_p-spaces associated to semifinite von Neumann algebras admit positive trace-preserving maps for which basic norm and duality properties, strict norm inequalities, and Schatten-ideal compactness criteria can be established in the same manner as classical cases (abstract, first paragraph).

C3one line summary

Introduces and develops the theory of quantum doubly stochastic operators on non-commutative L_p-spaces, establishing norm properties, compactness criteria, and applications to quantum majorization.

References

26 extracted · 26 resolved · 0 Pith anchors

[1] P. M. Alberti and A. Uhlmann,Stochasticity and Partial Order: Doubly Stochastic Maps and Unitary Mixing, North-Holland Math. Library, Vol. 18, North-Holland, Amsterdam, 1982 1982

[2] Ando,Majorization, doubly stochastic matrices, and comparison of eigenvalues, Linear Algebra Appl.118(1989), 163–248 1989

[3] J. Bergh and J. L¨ ofstr¨ om,Interpolation Spaces: An Introduction, Springer, Berlin, 1976 1976

[4] Bhatia,A note on the Lyapunov equation, Linear Algebra Appl.259(1997), 71–76 1997

[5] Birkhoff,Tr` es theoremes sur les matrices stochastiques, Proc 1946

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:54.133446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f5d0afbd38536e139640215b96b658bd98e15db3863cfcae5c24322510653f5

Aliases

arxiv: 2605.17711 · arxiv_version: 2605.17711v1 · doi: 10.48550/arxiv.2605.17711 · pith_short_12: R5OQV66TQU3O · pith_short_16: R5OQV66TQU3OCOLE · pith_short_8: R5OQV66T

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/R5OQV66TQU3OCOLEAIK3S23FRP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8f5d0afbd38536e139640215b96b658bd98e15db3863cfcae5c24322510653f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca522ccd4679512844027277b7d085d328bd322113461a45286be281e2a4e9cf",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-18T00:22:59Z",
    "title_canon_sha256": "defa5e4219f6a61d53c65072a80cc692951e68c42891ebb6c7a2160920c0cbec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17711",
    "kind": "arxiv",
    "version": 1
  }
}