Vol. 137, No. 1, 1989

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An addition formula for the index of semigroups of endomorphisms of B(H)

William Arveson

Vol. 137 (1989), No. 1, 19–36
Abstract

It is shown that the numerical index d(α) of a semigroup α of -endomorphisms of B(H) obeys the logarithmic addition formula

d∗(α ⊗ β) = d∗(α)+ d∗(β ).

The proof makes essential use of the theory of continuous product systems

Mathematical Subject Classification 2000
Primary: 47D25, 47D25
Secondary: 46L99, 47D05
Milestones
Received: 15 March 1988
Published: 1 March 1989
Authors
William Arveson
Department of Mathematics
University of California, Berkeley
Berkeley CA 94720
United States
http://math.berkeley.edu/~arveson/