Pith Number

pith:GVU42RRC

pith:2026:GVU42RRCCCLLPHEBVCRRKPCINH

not attested not anchored not stored refs resolved

Kadison's problem for trace-vector orthonormal bases in $\mathrm{II}_1$ factors with separable predual

Quanyu Tang, Teng Zhang, Yixin He

Diffuse finite von Neumann algebras with separable L2 admit orthonormal bases of self-adjoint unitaries.

arxiv:2605.15006 v1 · 2026-05-14 · math.OA

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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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Claims

C1strongest claim

if M is a diffuse finite von Neumann algebra with faithful normal tracial state τ and L²(M,τ) is separable, then L²(M,τ) admits an orthonormal basis consisting of self-adjoint unitaries in M. Consequently, we affirm the separable case of the Kadison problem.

C2weakest assumption

The Akemann-Weaver noncommutative Lyapunov theorem can be applied to the specific finite-dimensional orthogonality constraints that arise at each iterative step, and the reduced algebra after removing the span of the chosen symmetries remains diffuse so that the process can continue indefinitely.

C3one line summary

Every diffuse finite von Neumann algebra with separable L2 space has an orthonormal basis of self-adjoint unitaries with respect to the trace.

References

7 extracted · 7 resolved · 0 Pith anchors

[1] C. A. Akemann and N. Weaver, Automatic convexity, J. Convex Anal. 10 (2003), no. 1, 275--284. https://www.heldermann-verlag.de/jca/jca10/jca0339.pdf 2003

[2] Ching, Free products of von Neumann algebras, Trans 1973 · doi:10.1090/s0002-9947-1973-0326405-3

[3] M. Choda, Shifts on the hyperfinite II_1 -factor , J. Operator Theory 17 (1987), no. 2, 223--235. https://www.jstor.org/stable/24714840 1987

[4] D. De and K. Mukherjee, On the existence of uniformly bounded self-adjoint bases in GNS spaces, Doc. Math. 28 (2023), 1381--1392. doi:10.4171/DM/941 2023 · doi:10.4171/dm/941

[5] L. M. Ge, On ``Problems on von Neumann Algebras by R. Kadison, 1967'', Acta Math. Sin. (Engl. Ser.) 19 (2003), no. 3, 619--624. doi:10.1007/s10114-003-0279-x 1967 · doi:10.1007/s10114-003-0279-x

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:54.866716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3569cd46221096b79c81a8a3153c4869e95527f1c952e44c9337e1ade551b94f

Aliases

arxiv: 2605.15006 · arxiv_version: 2605.15006v1 · doi: 10.48550/arxiv.2605.15006 · pith_short_12: GVU42RRCCCLL · pith_short_16: GVU42RRCCCLLPHEB · pith_short_8: GVU42RRC

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GVU42RRCCCLLPHEBVCRRKPCINH \
  | 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: 3569cd46221096b79c81a8a3153c4869e95527f1c952e44c9337e1ade551b94f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69dc2bd519b7747907da1a30cb6dd6a56da92abb8be550b26203fc75fb6d3f8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-14T16:07:06Z",
    "title_canon_sha256": "ec8dce15a4e8008fbf3b067baee6ad1a1cbd8e99e1d847d85939c7c30e9e3ac4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15006",
    "kind": "arxiv",
    "version": 1
  }
}