Invertible Classes

SOME REMARKS ON WEAKLY INVERTIBLE FUNCTIONS IN THE UNIT BALL AND POLYDISK

We will present an approach to deal with a problem of existence of (not) weakly invertible functions in various spaces of analytic functions in the unit ball and polydisk based on estimates for integral operators acting between functional classes of different dimensions.

Some equivalence classes of operators on B(H)

Intervals of Certain Classes of Z-matrices

Let A and B be M -matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M -matrix and B is an invertible M matrix and A ≤ B, then aA+ bB is an invertible M -matrix for all a, b > 0. In this article, we present an elementary proof of a stronger version of this result and study correspon...

On the number of equivalence classes of invertible Boolean functions under action of permutation of variables on domain and range

Let Vn be the number of equivalence classes of invertible maps from {0,1}n to {0,1}n, under action of permutation of variables on domain and range. So far, the values Vn have been known for n 6 6. This paper describes the procedure by which the values of Vn are calculated for n 6 30.

On Unit-Central Rings

We establish commutativity theorems for certain classes of rings in which every invertible element is central, or, more generally, in which all invertible elements commute with one another. We prove that if R is a semiexchange ring (i.e. its factor ring modulo its Jacobson radical is an exchange ring) with all invertible elements central, then R is commutative. We also prove that if R is a semi...

Stability of Flip and Exchange Symmetric Entangled State Classes under Invertible Local Operations

Flip and exchange symmetric (FES) many-qubit states, which can be obtained from a state with the same symmetries by means of invertible local operations (ILO), constitute a one-parameter family of curves in the Hilbert space. Eigenstates of FES ILOs correspond to vectors that cannot be transformed to other FES states. This means equivalence classes of states under ILO can be determined in a sys...