Exercise 8, § 4

Extend Exercises 7, 8 and 9 of Chapter VI, § 3 to the spaces $W_{n,p}$ (no. 4). In the vector space $\mathbf{H}^n$ over the division ring of quaternions, we again denote by $W_{n,p}$ the set of all sequences $(x_k)_{1 \leq k \leq p}$ of $p$ vectors $x_k = (x_{kj})_{1 \leq j \leq n}$ such that

and ($\overline{x}$ denoting the conjugate of the quaternion $x$). Extend Exercises 7, 8 and 9 of Chapter VI, § 3, to these spaces $W_{n,p}$.