| Popis: |
We study constructions of ideals in the Fourier-Stieltjes algebra B ( G ) that are related to L p ( G ) . For 1 ≤ p ∞ , these constructions include the norm and weak*-closures of span ( P ( G ) ∩ L p ( G ) ) and B ( G ) ∩ L p ( G ) inside of B ( G ) , where P ( G ) denotes the set of positive definite functions on G. Previous results of the third author on these spaces are generalized. We obtain partial affirmative results regarding the equality of the norm closures (resp., weak* closures) of the two spaces listed above. In particular, we affirmatively answer a question of Kaliszewski, Landstad, and Quigg regarding SL ( 2 , R ) . Considering the existence of bounded approximate identities and Δ-weak approximate identities, we construct a counter-example to a misstatement in the literature regarding BSE-algebras contained in the Rajchman algebra B 0 ( G ) . Along the way, it is noted that there exist locally compact groups G so that the map [ 2 , ∞ ) ∋ p ↦ ‖ f ‖ L p , BG is discontinuous for some f ∈ L 1 ( G ) , where ‖ ⋅ ‖ L p , BG denotes the L p -C*-norms on L 1 ( G ) first introduced by Brown and Guentner. |
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