TY - JOUR
AU - S Sundar,
PY - 2022/10/12
Y2 - 2022/12/08
TI - On a Theorem of Cooper
JF - New Zealand Journal of Mathematics
JA - NZ J Math
VL - 53
IS -
SE - Articles
DO - 10.53733/197
UR - https://nzjmath.org/index.php/NZJMATH/article/view/197
SP - 11--25
AB - <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><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></div></div></div>
ER -