Pith Number

pith:OFUEZF7J

pith:2026:OFUEZF7J5FZBQYC3BQXIONN6MS

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Relative Kubo-Ando Means of Completely Positive Maps

Mohsen Kian

Relative and intrinsic Kubo-Ando means extend operator means to completely positive maps on C*-algebras via Arveson's Radon-Nikodym theorem.

arxiv:2605.11701 v2 · 2026-05-12 · math.OA · math.FA

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Claims

C1strongest claim

We introduce relative and intrinsic Kubo--Ando means for completely positive maps on C*-algebras. These means extend the usual Kubo--Ando means of positive operators and are defined using Arveson's Radon--Nikodym theorem for completely positive maps. We prove their basic order-theoretic properties, including monotonicity, transformer and Jensen inequalities, data processing, and monotonicity with respect to the ambient map.

C2weakest assumption

Arveson's Radon-Nikodym theorem applies directly to the pairs of completely positive maps under consideration and yields a well-defined derivative that can be used to construct the means without additional restrictions.

C3one line summary

Relative and intrinsic Kubo-Ando means are introduced for completely positive maps, satisfying order properties and reducing to prior means on matrix algebras and common domains.

Formal links

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Receipt and verification

First computed	2026-05-20T00:05:47.128737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71684c97e9e97218605b0c2e8735be649ba789d56ab7a1cc8ba97e532922dbe1

Aliases

arxiv: 2605.11701 · arxiv_version: 2605.11701v2 · doi: 10.48550/arxiv.2605.11701 · pith_short_12: OFUEZF7J5FZB · pith_short_16: OFUEZF7J5FZBQYC3 · pith_short_8: OFUEZF7J

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OFUEZF7J5FZBQYC3BQXIONN6MS \
  | 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: 71684c97e9e97218605b0c2e8735be649ba789d56ab7a1cc8ba97e532922dbe1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0585dab00aef312bec7df8c909ec1a88ad970d11e01197f6b81afb09aed57338",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-12T07:58:03Z",
    "title_canon_sha256": "3a354a2330ae4647a9327f0e08839975b3aa7579c1767c55c86227ce19500af0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11701",
    "kind": "arxiv",
    "version": 2
  }
}