  Motivated by importance of operator spaces contained in the set of all scalar
multiples of isometries ($MI$-spaces) in a separable Hilbert space for
$C^*$-algebras and E-semigroups we exhibit more properties of such spaces. For
example, if an $MI$-space contains an isometry with shift part of finite
multiplicity, then it is one-dimensional. We propose a simple model of a
unilateral shift of arbitrary multiplicity and show that each separable
subspace of a Hilbert space is the range of a shift. Also, we show that
$MI$-spaces are non-symmetric, very unfriendly to multiplication, and prove a
Commutator Identity which elucidates the extreme non-commutativity of these
spaces.
