Unitaries and partial isometries in a real 𝑊*-algebra

Abstract

The group of unitaries in a real <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper W Superscript asterisk"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{W^{\ast }}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebra without a finite type I direct summand is connected. This fact is used to characterize the components of the set of partial isometries in such algebras.

Locations

• Proceedings of the American Mathematical Society - View - PDF