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Shifts of group-like projections and contractive idempotent functionals for locally compact quantum groups

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cris.lastimport.scopus2024-02-12T20:28:04Z
dc.abstract.enA one-to-one correspondence between shifts of group-like projections on a locally compact quantum group G ?? which are preserved by the scaling group and contractive idempotent functionals on the dual Gˆ??̂ is established. This is a generalization of the Illie–Spronk’s correspondence between contractive idempotents in the Fourier–Stieltjes algebra of a locally compact group GG and cosets of open subgroups of GG. We also establish a one-to-one correspondence between nondegenerate, integrable, G??-invariant ternary rings of operators X⊂L∞(G) X⊂L∞(??), preserved by the scaling group and contractive idempotent functionals on G??. Using our results, we characterize coideals in L∞(Gˆ) L∞(??̂) admitting an atom preserved by the scaling group in terms of idempotent states on G??. We also establish a one-to-one correspondence between integrable coideals in L∞(G)L∞(??) and group-like projections in L∞(Gˆ) L∞(??̂) satisfying an extra mild condition. Exploiting this correspondence, we give examples of group-like projections which are not preserved by the scaling group.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorKasprzak, Paweł
dc.date.accessioned2024-01-26T07:35:54Z
dc.date.available2024-01-26T07:35:54Z
dc.date.issued2018
dc.description.financeNie dotyczy
dc.description.number13
dc.description.volume29
dc.identifier.doi10.1142/S0129167X18500921
dc.identifier.issn0129-167X
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/119752
dc.identifier.weblinkhttps://www.worldscientific.com/doi/abs/10.1142/S0129167X18500921
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofInternational Journal of Mathematics
dc.relation.pages1850092: 1-19
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enContractive idempotent functionals on quantum groups
dc.subject.enshifts of group-like projections
dc.subject.enternary ring of operators
dc.titleShifts of group-like projections and contractive idempotent functionals for locally compact quantum groups
dc.typeJournalArticle
dspace.entity.typePublication