Tolerances and Commutators on lattices

Orthomodular lattices with fully nontrivial commutators

An orthomodular lattice L is said to have fully nontrivial commutator if the commutator of any pair x, y ∈ L is different from zero. In this note we consider the class of all orthomodular lattices with fully nontrivial commutators. We show that this class forms a quasivariety, we describe it in terms of quasiidentities and situate important types of orthomodular lattices (free lattices, Hilbert...

On Commutators of Isometries and Hyponormal Operators

A sufficient condition is obtained for two isometries to be unitarily equivalent. Also, a new class of M-hyponormal operator is constructed

Commutators on ` ∞

The operators on `∞ which are commutators are those not of the form λI + S with λ 6= 0 and S strictly singular.

On Commutators and Jacobi Matrices1

The closure, W, oí the set of values (Cx, x) when ||x|| = 1 is a closed convex set (Hausdorff, cf. [8, p. 34]). A complex number z will be said to belong to the interior of W if z is in W and if one of the following conditions holds: (i) If W is two-dimensional, then z does not lie on the boundary of W; (ii) If IF is a line segment, then z is not an end point; (iii) W consists of z alone. It wa...

On Subgroup Commutators