Space form isometries as commutators and products of involutions

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

Powers of Commutators as Products of Squares

Square-free words as products of commutators

Elements of the commutator subgroup of a free group F can be presented as values of canonical forms, called Wicks forms. We show that, starting from sufficiently high genus g, there is a sequence of words wg which can be presented by f .g/ distinct Wicks forms, where f .g/ > gŠ. Moreover we may choose these words wg to be square-free. Mathematics Subject Classification (2000). 20E05, 20F10.

Powers of a product of commutators as products of squares

We prove that for any odd integer N and any integer n > 0, the Nth power of a product of n commutators in a nonabelian free group of countable infinite rank can be expressed as a product of squares of 2n+1 elements and, for all such odd N and integers n, there are commutators for which the number 2n+1 of squares is the minimum number such that the Nth power of its product can be written as a pr...

Isometries of Cross Products of Sequence Spaces

Let X0, X1, . . . , Xk with k ∈ IN ∪ {∞} be sequence spaces (finite or infinite dimensional) over C or IR with absolute norms Ni for i = 0, . . . , k, (i.e., with 1unconditional bases) such that dimX0 = k. Define an absolute norm on the cross product space (also known as the X0 1-unconditional sum) X1 × · · · ×Xk by N(x1, . . . , xk) = N0(N1(x1), . . . , Nk(xk)) for all (x1, . . . , xk) ∈ X1 × ...