In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R...

We refine the recent local rigidity result for marked length spectrum obtained by first and third author in \cite{Guillarmou-Lefeuvre-18} give an alternative proof using geodesic stretch between two Anosov flows some uniform estimate on variance appearing central limit theorem flows. In turn, we also introduce a new pressure metric space of isometry classes, that reduces to Weil-Peterson case T...

We consider the question of estimating a real low-complexity signal (such as sparse vector or low-rank matrix) from phase complex random measurements. show that in this phase-only compressive sensing (PO-CS) scenario, we can perfectly recover such with high probability and up to global unknown amplitude if matrix is Gaussian number measurements large compared complexity level space. Our approac...

Let M and N be two unital JB∗-algebras let U(M) U(N) denote the sets of all unitaries in N, respectively. We prove that following statements are equivalent: isometrically isomorphic as (complex) Banach spaces;M real spaces;there exists a surjective isometry Δ:U(M)→U(N).We actually establish more general statement asserting that, under some mild extra conditions, for each Δ:U(M)→U(N), we can fin...

Let M and N be complex unital Jordan-Banach algebras, let M−1 N−1 denote the sets of invertible elements in N, respectively. Suppose that M⊆M−1 N⊆N−1 are clopen subsets N−1, respectively, which closed for powers, inverses products form Ua(b). In this paper we prove each surjective isometry Δ:M→N there exists a real-linear T0:M→N an element u0 McCrimmon radical such Δ(a)=T0(a)+u0 all a∈M. Assumi...

Abstract Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the concept of an asymptotically linear estimator and the associated influence function leads to optimal sampling procedures for a wide class of popula...

In this paper we continue the investigation into the group of algebras with uniformly distributed invariants, U(k’), and its relation to the Schur subgroup S(K), undertaken in [6, 71. We maintain the notation of [6, 71. In the first section we investigate U(K) for a real quadratic field K. We calculate generators of U(K) explicitly. In the second section we investigate U(K) for other real field...