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Isometries of quasitriangular operator algebras

Authors: Alan Hopenwasser and Joan Plastiras
Journal: Proc. Amer. Math. Soc. 65 (1977), 242-244
MSC: Primary 46L15
MathSciNet review: 0448111
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Abstract: Let $ ({P_n})$ be an increasing sequence of finite rank projections on a separable Hilbert space. Assume $ {P_n}$ converges strongly to the identity operator I. The quasitriangular operator algebra determined by $ ({P_n})$ is defined to be the set of all bounded linear operators T for which

$\displaystyle \mathop {\lim }\limits_{x \to \infty } \left\Vert {(I - {P_n})T{P_n}} \right\Vert = 0.$

In this note we prove that two quasitriangular algebras are unitarily equivalent if, and only if, there exists a unital linear isometry mapping one algebra onto the other.

References [Enhancements On Off] (What's this?)

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