@article{S Sundar_2022, title={On a Theorem of Cooper}, volume={53}, url={https://nzjmath.org/index.php/NZJMATH/article/view/197}, DOI={10.53733/197}, abstractNote={<div class="page" title="Page 1">
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<p>The classical result of Cooper states that every pure strongly continuous semigroup of isometries $\{V_t\}_{t \geq 0}$ on a Hilbert space is unitarily equivalent to the shift semigroup on $L^{2}([0,\infty))$ with some multiplicity. <br />The purpose of this note is to record a proof which has an algebraic flavour. The proof is based on the groupoid approach to semigroups of isometries initiated in [8]. We also indicate how our proof can be adapted to the Hilbert module setting and gives another proof of the main result of [3]. </p>
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</div>}, journal={New Zealand Journal of Mathematics}, author={S Sundar}, year={2022}, month={Oct.}, pages={11–25} }