Strict isometries of arbitrary orders

Strict Isometries of Arbitray Orders

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 ...

Partial Orders on Partial Isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spac...

Strict orders prohibit elimination of hyperimaginaries

A theory with the strict order property does not eliminate hyperimaginaries. Hence a theory without the independence property eliminates hyperimaginaries if and only if it is stable. A type definable equivalence relation is an equivalence relation on tuples of a certain length (possibly infinite) which is defined by a partial type E(x̄; ȳ) over ∅. A hyperimaginary is an equivalence class ā/E. If...

Perturbative Gadgets at Arbitrary Orders

Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactio...

Approximation Orders for Natural Splines in Arbitrary