span (A(1),..., A(n)) denotes the linear space spanned by Hilbert space operators A(1),..., A(n). It is known that if span (A, B) consists of normal operators, then A, B commute. Let MI denote the set of all scalar multiples of all isometries in a Hilbert space H. In this paper finite-dimensional linear spaces contained in MI will be investigated. Commutativity of such spaces will be described. An example will be given of two unilateral shifts A, B of infinite multiplicity such that span (A, B) subset of MI and A, B do not commute.
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