Pith Number

pith:PL5QNG6G

pith:2026:PL5QNG6G5WMPIDX2ZEPIUGQ67A

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On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras

Jekwin J. Dabhi, Prakash A. Dabhi

Semisimple commutative Banach algebras have either a unique uniform norm or uncountably many, plus a largest weakly regular closed subalgebra and largest closed ideals with UUNP and SEP.

arxiv:2605.18179 v1 · 2026-05-18 · math.FA

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\usepackage{pith}
\pithnumber{PL5QNG6G5WMPIDX2ZEPIUGQ67A}

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Record completeness

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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

Let A be a semisimple commutative Banach algebra. It is shown that either A has exactly one uniform norm or it admits uncountably many uniform norms.

C2weakest assumption

The algebra A is assumed to be semisimple (Jacobson radical is zero) and commutative, which is the setting stated at the start of the abstract for all subsequent claims about uniform norms and maximal substructures.

C3one line summary

Semisimple commutative Banach algebras have either a unique uniform norm or uncountably many, plus a largest weakly regular closed subalgebra and largest closed ideals with UUNP and SEP.

Receipt and verification

First computed	2026-05-20T00:05:49.491945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7afb069bc6ed98f40efac91e8a1a1ef80683013bb84c680b6c579aecb67754e8

Aliases

arxiv: 2605.18179 · arxiv_version: 2605.18179v1 · doi: 10.48550/arxiv.2605.18179 · pith_short_12: PL5QNG6G5WMP · pith_short_16: PL5QNG6G5WMPIDX2 · pith_short_8: PL5QNG6G

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PL5QNG6G5WMPIDX2ZEPIUGQ67A \
  | 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: 7afb069bc6ed98f40efac91e8a1a1ef80683013bb84c680b6c579aecb67754e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e57cc67581f0193f97fadf90d3de08275c0bb80d2368352955dbf0396873396e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-18T10:21:19Z",
    "title_canon_sha256": "7f27c1ec4f881592ab4f38b35b53ef67a5d3954df30e6f3dc262340c8f6bc90e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18179",
    "kind": "arxiv",
    "version": 1
  }
}