Let (X,d,m) be a compact non-branching metric measure space equipped with a qualitatively non-degenerate measure m. The study of properties of the Lp–Wasserstein space (Pp(X),Wp) associated to X has ...proved useful in describing several geometrical properties of X. In this paper we focus on the study of isometries of Pp(X) for p∈(1,∞) under the assumption that there is some characterization of optimal maps between measures, the so called Good Transport Behaviour GTBp. Our first result states that the set of Dirac deltas is invariant under isometries of the Lp–Wasserstein space. Additionally, for Riemannian manifolds we obtain that the isometry groups of the Lp–Wasserstein space and of the base space coincide under geometric assumptions on the manifold; namely, for p=2 that the sectional curvature is strictly positive and for general p∈(1,∞) that the Riemannian manifold is a Compact Rank One Symmetric Space.
Suppose that a compact quantum group Q acts faithfully on a smooth, compact, connected manifold M, i.e. has a C⁎ (co)-action α on C(M), such that α(C∞(M))⊆C∞(M,Q) and the linear span of α(C∞(M))(1⊗Q) ...is dense in C∞(M,Q) with respect to the Fréchet topology. It was conjectured by the author quite a few years ago that Q must be commutative as a C⁎ algebra i.e. Q≅C(G) for some compact group G acting smoothly on M. The goal of this paper is to prove the truth of this conjecture. A remarkable aspect of the proof is the use of probabilistic techniques involving Brownian stopping time.
The MacWilliams' Extension Theorem (MET) with respect to a combinatorial metric states that every isomorphism between linear codes that preserves combinatorial weight can be extended to an isometric ...extension of the whole space. Pinheiro et al. (2019) proposed the problem of characterizing combinatorial metrics over a finite field with two elements that admit the MET. In this paper, we provide the complete description of such metrics.
For any 1 ≤ p ≤ ∞, let S
p
(
) be the space of holomorphic functions f on
such that f′ belongs to the Hardy space H
p
(
), with the norm ∥f∥
∑
= ||f||
∞
+||f′||
p
. We prove that every approximate ...local isometry of S
p
(
) is a surjective isometry and that every approximate 2-local isometry of S
p
(
) is a surjective linear isometry. As a consequence, we deduce that the sets of isometric reflections and generalized bi-circular projections on S
p
(
) are also topologically reflexive and 2-topologically reflexive.
Hopf coactions on odd spheres Bhattacharjee, Suvrajit; Goswami, Debashish
Journal of algebra,
12/2019, Letnik:
539
Journal Article
Recenzirano
Odprti dostop
We prove that the q-deformed unitary group, i.e., Uq(N), is the universal compact quantum group in the category of (compact) quantum groups which coact on the q-deformed odd sphere Sq2N−1 leaving the ...space spanned by the natural set of generators invariant and preserving the unique SUq(N) invariant functional on Sq2N−1. Using this, we identify Uq(N) as the quantum group of orientation preserving isometries (in the sense of Bhowmick and Goswami 5) for a natural spectral triple associated with Sq2N−1 constructed by Chakraborty and Pal 9.
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