Gleason–Kahane–Żelazko theorem
theorem that a nonzero linear functional on a unital complex Banach algebra is multiplicative iff it maps each element of the Banach algebra to an element of its spectrum
| rdfs:label |
"Gleason–Kahane–Żelazko theorem"@en
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skos:alt |
"Gleason-Kahane-Żelazko theorem"@en
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| schema:description |
"theorem that a nonzero linear functional on a unital complex Banach algebra is multiplicative iff it maps each element of the Banach algebra to an element of its spectrum"@en
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schema:date |
"2026-09-07T08:05:59+00:00"^^xsd:dateTime |
| schema:version | 2541582830 |
| wikibase:identifiers | 1 |
| wikibase:sitelinks | 3 |
| wikibase:statements | 8 |
| p:P138 | wd:statement/Q2226660-69ce446f-4b2b-07a0-9968-c29a5ab22b8d |
| wd:statement/Q2226660-7046ec2e-4273-bf9b-f791-1dfe80905ec3 | |
| wd:statement/Q2226660-a54848e2-447e-4818-8b74-2213674a4dcc | |
| p:P2534 | wd:statement/Q2226660-f86f03af-4008-fee0-41a5-a9ad4a0f50c3 |
| p:P2579 | wd:statement/Q2226660-b77d56d3-425d-92f0-6c27-2fed2729be75 |
| p:P2671 | wd:statement/Q2226660-8058BAAD-609C-48EC-936D-A131A6845B30 |
| p:P31 | wd:statement/Q2226660-362a1ad6-4bf9-43f5-a5b5-fdaff4eaed07 |
| p:P6104 | wd:statement/Q2226660-E4430399-1407-47A3-9D9F-69BE384F837F |
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p:direct- |
<http:/ |
| wdt:P138 | Andrew Gleason |
| Jean-Pierre Kahane | |
| Wiesław Żelazko | |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">≠</mo><mn>0</mn><mo stretchy="false">∧</mo><mi mathvariant="normal">∀</mi><mi>a</mi><mo>,</mo><mi>b</mi><mo stretchy="false">∈</mo><mi>A</mi><mo stretchy="false">:</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">∈</mo><mi>A</mi><mo stretchy="false">:</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>σ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | functional analysis |
| wdt:P2671 | "/g/120scz93" |
| wdt:P31 | theorem |
| wdt:P6104 | WikiProject Mathematics |
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