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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Continuous spatial semigroups of $*$-endomorphisms of $\mathfrak {B}(\mathfrak {H})$
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by Robert T. Powers and Geoffrey Price PDF
Trans. Amer. Math. Soc. 321 (1990), 347-361 Request permission

Abstract:

To each continuous semigroup of $*$-endomorphisms $\alpha$ of $\mathfrak {B}\left ( \mathfrak {H} \right )$ with an intertwining semigroup of isometries there is associated a $*$-representation $\pi$ of the domain $\mathfrak {O}(\delta )$ of the generator of $\alpha$. It is shown that the Arveson index ${d_ * }(\alpha )$ is the number of times the representation $\pi$ contains the identity representation of $\mathfrak {O}(\delta )$. This result is obtained from an analysis of the relation between two semigroups of isometries, $U$ and $S$, satisfying the condition $S{(t)^*}U(t) = {e^{ - \lambda t}}I$ for $t \geq 0$ and $\lambda > 0$.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 321 (1990), 347-361
  • MSC: Primary 47D25; Secondary 46L99, 47D05
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0974524-0
  • MathSciNet review: 974524