We consider the elementary operator L, acting on the Hilbert-Schmidt Class C2(H), given by L(T ) = ATB, with A and B bounded operators on a separable Hilbert space H. In this paper we establish results relating isometric properties of L with those of the defining symbols A and B. We also show that if A is a strict n−isometry on a Hilbert space H then {I, A∗A, (A∗)2A2, . . . , (A∗)n−1An−1} is a ...

We calculate the scalar potential in the gauged N=2 supergravity with a single hypermultiplet, whose generic quaternionic moduli space metric has an abelian isometry. This isometry is gauged by the use of a graviphoton gauge field. The hypermultiplet metric and the scalar potential are both governed by the single real potential that is a solution to the 3d (integrable) continuous Toda equation....

| In the cryptanalysis of stream ciphers and pseudorandom sequences, the notions of linear, jump, and 2{adic complexity arise naturally to measure the (non)randomness of a given string. We de ne an isometry K on Fq that is the precise equivalent to Euclid’s algorithm over the reals to calculate the continued fraction expansion of a formal power series. The continued fraction expansion allows to...

Abstract We give necessary and sufficient conditions on an m -isometry to have invertible -isometrical extension. As particular cases, we a useful characterization for general unilateral weighted shift $$\ell $$ ℓ -Jordan isometries. In particular, every isometry operator has $$(2\ell -1)$$ <mml:mo...

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL(2,R) × U(1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

The near-horizon geometries of the extremal Kerr black hole and certain generalizations thereof are considered. Their isometry groups are all given by SL(2,R) × U(1). The usual boundary conditions of the Kerr/CFT correspondence enhance the U(1) isometry to a Virasoro algebra. Various alternatives to these boundary conditions are discussed. Partial classifications are provided of the boundary co...

In previous work, numerical experiments showed that ` minimization with 0 < p < 1 recovers sparse signals from fewer linear measurements than does ` minimization. It was also shown that a weaker restricted isometry property is sufficient to guarantee perfect recovery in the ` case. In this work, we generalize this result to an ` variant of the restricted isometry property, and then determine ho...

The isometry group of a compact n-dimensional hyperbolic man-ifold is known to be finite. We show that for every n ≥ 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proven by Greenberg [G] and Ko-jima [K], respectively. Our proof is non constructive: it uses counting results from subgroup growth theory to sh...