Pith Number

pith:NQH5WL46

pith:2026:NQH5WL46VM3JJYMG7PNPETLPXM

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Strongly Integrable Operator-Valued Functions, Generated Vector Measures and Compactness of Integrals

Matija Milovi\'c, Mihailo Krsti\'c, Milo\v{s} Arsenovi\'c, Stefan Milo\v{s}evi\'c

Every strongly integrable operator-valued function generates a countably additive B(X,Y)-valued measure in the operator norm when X* contains no copy of c0.

arxiv:2605.12454 v2 · 2026-05-12 · math.FA

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

every function in L_s^1(Ω,μ, B(X,Y)) generates a countably additive, in operator norm, B(X,Y)-valued measure whenever X* does not contain an isomorphic copy of c0

C2weakest assumption

The assumption that X* does not contain an isomorphic copy of c0 is load-bearing for the key theorem on generating countably additive measures; without it the measure may fail to be countably additive in norm, and the downstream compactness and spectral results would not follow.

C3one line summary

Strongly integrable operator-valued functions generate norm-countably additive measures when X* avoids c0, so their integrals of compact operators are compact when X avoids ℓ1, plus a spectral radius inequality for commuting families.

Receipt and verification

First computed	2026-05-20T00:04:36.516062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c0fdb2f9eab3694e186fbdaf24d6fbb0bb50a50ecb42f3b3f7630418f95dee5

Aliases

arxiv: 2605.12454 · arxiv_version: 2605.12454v2 · doi: 10.48550/arxiv.2605.12454 · pith_short_12: NQH5WL46VM3J · pith_short_16: NQH5WL46VM3JJYMG · pith_short_8: NQH5WL46

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NQH5WL46VM3JJYMG7PNPETLPXM \
  | 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: 6c0fdb2f9eab3694e186fbdaf24d6fbb0bb50a50ecb42f3b3f7630418f95dee5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bec1ae7ab24dfd32bdf5d09d87e68401d6c7e8ef383881e2c521765b13b3b632",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-12T17:43:58Z",
    "title_canon_sha256": "23c12eab3ffe1281841e4e14064080532d6e18707f4e644a90d0071051da0aed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12454",
    "kind": "arxiv",
    "version": 2
  }
}