Abstract: The classical Weyl-von Neumann theorem states that for any selfadjoint operator A in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C = C∗ such that the perturbed operator A + C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely define...

If m is a positive integer, let ǫk = e 2kπi/m for k = 1, . . . ,m. Then ǫk = 1 (k = 1, . . . ,m), ǫk 6= 1 (k = 1, . . . ,m− 1) and ǫm = 1 . If a ∈ A is invertible, define the bounded linear operator Ta : A → A by Tax = a xa (x ∈ A) . Proposition 1. Suppose that a ∈ A is invertible, m is a positive integer and that σ(a) is irrotational (mod 2π/m). Let the bounded linear operator S : A → A be giv...

We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superal...

The paper presents a new definition of closure operator which encompasses the standard Dikranjan-Giuli notion, as well as the Bourn-Gran notion of normal closure operator. As is well known, any two closure operators C,D in a category may be composed in two ways: For a subobject M → X one may consider DX(CXM) or DCX(M)(M) as the value at M of a new closure operator D ·C or D ∗C, respectively. Th...

In [14] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. The construction leading to the pair of dually (order) isomorphic lattices can be further manipulated to obtain the three other types of Galois Connections pro...