On subgroup commutators

On Subgroup Commutators

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 in Groups

Commutators originated over 100 years ago as a by-product of computing group characters of nonabelian groups. They are now an established and immensely useful tool in all of group theory. Commutators became objects of interest in their own right soon after their introduction. In particular, the phenomenon that the set of commutators does not necessarily form a subgroup has been well documented ...

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

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...