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The shiftable Heffter arrays are naturally generalized to the shiftable Heffter spaces. We present a recursive construction which starting from a single shiftable Heffter space leads to infinitely many other shiftable Heffter spaces of the…
In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.
It is shown that any separable state on Hilbert space ${\cal H}={\cal H}_1\otimes{\cal H}_2$, can be written as a convex combination of N pure product states with $N\leq (dim{\cal H})^2$. Then a new separability criterion for mixed states…
An ideal system of $n$ qubits has $2^n$ dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
We introduce the concept of a \mu-scale invariant operator with respect to unitary transformation in a separable complex Hilbert space. We show that if a nonnegative densely defined symmetric operator is \mu-scale invariant for some \mu >0,…
This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU(2) corresponding to an irreducible representation of SU(2). The representation theory of SU(2)…
We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…
We investigate with the help of Clifford algebraic methods the Mandelbrot set over arbitrary two-component number systems. The complex numbers are regarded as operator spinors in D\times spin(2) resp. spin(2). The thereby induced (pseudo)…
A strictly increasing sequence (n_k) of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that the supremum over k of the norms ||T^{n_k}|| is finite, the set of…
The unitary group acting on the Hilbert space of three quantum bits admits a Lie subgroup, of elements which permute with the symmetric group of permutations. Under the action of such Lie subgroup, the Hilbert space splits into three…
A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the…
This is a continuation of our previous paper. We consider a certain order-like relation for positive operators on a Hilbert space. This relation is defined by using the Jensen inequality with respect to the square-root function. We show…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
We introduce a one-dimensional correlated-hopping model of spinless fermions in which a particle can hop between two neighboring sites only if the sites to the left and right of those two sites have different particle numbers. Using a…
Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the…
For every integer $k\geq 2$, we construct infinite families of mutually nondiffeomorphic irreducible smooth structures on the topological $4$-manifolds $(2k-1)(S^2\times S^2)$ and $(2k-1)(\CP#\CPb)$, the connected sums of $2k-1$ copies of…
On $4$-symmetric symplectic spaces, invariant almost complex structures -- up to sign -- arise in pairs. We exhibit some $4$-symmetric symplectic spaces, with a pair of "natural" compatible (usually not positive) invariant almost complex…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
The invariant subspace problem (ISP) is a well known unsolved problem in funtional analysis. While many partial results are known, the general case for complex, infinite dimensional separable Hilbert spaces is still open. It has been shown…