By Chunlan Jiang, Zhengwei Liu, Jinsong Wu
http://www.sciencedirect.com/science/article/pii/S0022123615003237
The classical uncertainty ideas care for capabilities on abelian teams. during this paper, we talk about the uncertainty rules for finite index subfactors which come with the situations for finite teams and finite dimensional Kac algebras. We turn out the Hausdorff–Young inequality, Young's inequality, the Hirschman–Beckner uncertainty precept, the Donoho–Stark uncertainty precept. We symbolize the minimizers of the uncertainty rules after which we turn out Hardy's uncertainty precept through the use of minimizers. We additionally end up that the minimizer is uniquely made up our minds via the helps of itself and its Fourier rework. The proofs take the good thing about the analytic and the categorial views of subfactor planar algebras. Our technique to turn out the uncertainty ideas additionally works for extra normal circumstances, akin to Popa's λ-lattices, modular tensor different types, and so on.
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Example text
Note that B is a central minimal projection in the group algebra of H, so its right shift Q is also a rank-one projection. Then tr 2 (hQ) , h ∈ H, tr 2 (Q) is a one dimensional representation of H. Take χ to be its contragredient representation, tr 2 (h−1 Q) 1 , and Q = then χ(h) = χ(h)h. Take x = h∈H χ(h)hg. Then R(x) = tr 2 Q |H| h∈H Q and R(F(x)) = Bg . So x is a bi-shift of a biprojection. 16, any bi-shift of a biprojection is of this form. ✷ Remark. Note that χ is the pull back of a character of H/[H, H], where [H, H] is the commutator subgroup.
V 21 δ1 δ3 . (12) So That is, (FP−1 (v))∗ (FP−1 (v)) ≤ ( 1 ,P3 1 ,P3 v 21 )1. δ1 δ3 Taking the norm on both sides, we have (FP−1 (v))∗ (FP−1 (v)) 1 ,P3 1 ,P3 ∞ ≤ v 21 . δ1 δ3 Hence FP−1 (v) 1 ,P3 ∞ Recall that FP1 ,P3 (v) = (FP−1 (v ∗ ))∗ and v 1 ,P3 v 1 ≤√ . δ1 δ3 1 = v ∗ 1 , we obtain that FP1 ,P3 (v) ∞ v 1 ≤√ . δ1 δ3 FP1 ,P3 (v) ∞ v 1 ≤√ . δ2 δ4 By symmetry, we have 304 C. Jiang et al. / Journal of Functional Analysis 270 (2016) 264–311 Therefore FP1 ,P3 (v) where δ0 = max{ δ1 δ3 , δ2 δ4 }.
C. Jiang et al. / Journal of Functional Analysis 270 (2016) 264–311 309 If there is a group action G on S, then the fixed point algebra of Spin under the induced group action of G is also a subfactor planar algebra, denoted by P . Moreover, P2,+ consists of S × S matrices commuting with the action of G. Let δ0 be the minimal n0 value of the trace of a nonzero minimal projection in P1,± . Then δ0 = √ , where n n0 is the minimal cardinality of G-orbits of S. Then we obtain the Hausdorff–Young inequality, Young’s inequality, the uncertainty principles, and the characterizations of minimizers for elements in P2,+ .