Pith Number

pith:EHDTHSAA

pith:2026:EHDTHSAAZMUNRIKCVNSJCALEQH

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Singular value functions for C\(^*\)-algebras

Naoto Fujitsu

Singular value functions can be defined for arbitrary C*-algebras and retain the main analytic features of classical singular values for compact operators.

arxiv:2605.17235 v1 · 2026-05-17 · math.FA · math.OA

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\pithnumber{EHDTHSAAZMUNRIKCVNSJCALEQH}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

We introduce singular value functions for C*-algebras, generalizing the singular values of compact operators on Hilbert spaces.

C2weakest assumption

That a consistent and useful generalization of singular values exists for arbitrary C*-algebras while preserving the key analytic properties that hold for compact operators on Hilbert space.

C3one line summary

The paper introduces singular value functions for C*-algebras that generalize singular values of compact operators and establishes their basic properties with examples.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Extending states on preordered semigroups and the existence of quasitraces on 1992 · doi:10.1016/0021-8693(92)90098-7

[2] Cuntz, Joachim , TITLE =. Math. Ann. , FJOURNAL =. 1978 , NUMBER =. doi:10.1007/BF01421922 , URL = 1978 · doi:10.1007/bf01421922

[3] and de Pagter, Ben and Sukochev, Fedor , TITLE = 2023 · doi:10.1007/978-3-031-49654-7

[4] and Handelman, David E 1980 · doi:10.2307/2374244

[5] Effros, Edward G. , TITLE =. 1981 , PAGES = 1981

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:46.805415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21c733c800cb28d8a142ab6491016481f9907747cc26e728a5bd1815ac4b7db5

Aliases

arxiv: 2605.17235 · arxiv_version: 2605.17235v1 · doi: 10.48550/arxiv.2605.17235 · pith_short_12: EHDTHSAAZMUN · pith_short_16: EHDTHSAAZMUNRIKC · pith_short_8: EHDTHSAA

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EHDTHSAAZMUNRIKCVNSJCALEQH \
  | 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: 21c733c800cb28d8a142ab6491016481f9907747cc26e728a5bd1815ac4b7db5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c943eaf79437f30ce7e15c6b217beaff188e4eb40cbbd038b29b6dacf9cdc831",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-17T03:16:25Z",
    "title_canon_sha256": "11a18f3a7917e9937bdaed7f83ce8a113273aa4afa569fc8ea82fe92ef9609e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17235",
    "kind": "arxiv",
    "version": 1
  }
}