Applications of Kazhdan's property (T) to automatic continuity

DOI10.1016/j.jmaa.2004.11.066zbMath1069.22002OpenAlexW2161903773MaRDI QIDQ555835

J. Extremera, Jerónimo Alaminos, Armando R. Villena

Publication date: 10 June 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.11.066

zbMATH Keywords

automatic continuityunitary representationsKazhdan's property Toperators commuting with translationsstrong Kazhdan's propertytranslation invariant linear functionals

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Automatic continuity (46H40) Groups and semigroups of linear operators (47D03) Linear operators on function spaces (general) (47B38) Other representations of locally compact groups (22D12)

Related Items (2)

On similarity of quasinilpotent operators ⋮ Cohen-Host type idempotent theorems for representations on Banach spaces and applications to Figà-Talamanca-Herz algebras

Cites Work

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• Automatic continuity is equivalent to uniqueness of invariant means
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• Some remarks on invariant means
• Difference spaces and invariant linear forms
• Kazhdan's property (T) for the unitary group of a separable Hilbert space
• Uniqueness of translation invariant norms
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• Invariant functionals and the uniqueness of invariant norms
• Translation-invariant linear forms and a formula for the Dirac measure
• Uniqueness of the topology on L¹(G)
• Translation-Invariant Linear Forms on L p (G)
• For 𝑛>3 there is only one finitely additive rotationally invariant measure on the 𝑛-sphere defined on all Lebesgue measurable subsets
• Invariant measures for algebraic actions, Zariski dense subgroups and Kazhdan’s property (T)

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