Continuous spatial semigroups of endomorphisms of
Authors:
Robert T. Powers and Geoffrey Price
Journal:
Trans. Amer. Math. Soc. 321 (1990), 347361
MSC:
Primary 47D25; Secondary 46L99, 47D05
MathSciNet review:
974524
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Abstract: To each continuous semigroup of endomorphisms of with an intertwining semigroup of isometries there is associated a representation of the domain of the generator of . It is shown that the Arveson index is the number of times the representation contains the identity representation of . This result is obtained from an analysis of the relation between two semigroups of isometries, and , satisfying the condition for and .
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 W. B. Arveson, An addition formula for the index of semigroups of endomorphisms of , Pacific J. Math. 137 (1989), 1936. MR 983326 (90c:47074)
 [A2]
 W. B. Arveson, Continuous analogues of Fock space, Mem. Amer. Math. Soc. (to appear). MR 987590 (90f:47061)
 [BHR]
 O. Bratteli, R. H. Herman, and D. W. Robinson, Perturbations of flows on Banach spaces and operator algebras, Comm. Math. Phys. 59 (1978), 167178. MR 491612 (80a:46038)
 [D1]
 R. G. Douglas, On the algebra of a oneparameter semigroup of isometries, Acta Math. 128 (1972), 143151. MR 0394296 (52:15099)
 [DS]
 N. Dunford and J. T. Schwartz, Linear operators, Interscience, New York, 1958; reprinted 1971.
 [P1]
 R. T. Powers, An index theory for semigroups of endomorphisms of and type factors, Canad. J. Math. 40 (1988), 86114. MR 928215 (89f:46116)
 [P2]
 , A nonspatial continuous semigroup of endomorphisms of , Publ. Res. Inst. Math. Sci. Kyoto Univ. 23 (1987), 10531069. MR 935715 (89f:46118)
 [PR]
 R. T. Powers and D. W. Robinson, An index for continuous semigroups of endomorphisms of , J. Funct. Anal. (to appear). MR 999489 (90f:46107)
 [RS]
 M. Reed and B. Simon, Methods of modern mathematical physics, Academic Press, New York, 1972. MR 0493419 (58:12429a)
 [RN]
 F. Riesz and B. Sz.Nagy, Functional analysis, Ungar, New York, 1955. MR 0071727 (17:175i)
 [R1]
 D. W. Robinson, The approximation of flows, J. Funct. Anal. 24 (1977), 280290. MR 0440420 (55:13295)
 [Sz]
 B. Sz.Nagy, Isometric flows in Hilbert space, Proc. Cambridge Phil. Soc. 60 (1964), 4549. MR 0159231 (28:2448)
 [Y1]
 K. Yosida, Functional analysis, SpringerVerlag, New York, 1974. MR 0350358 (50:2851)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199009745240
PII:
S 00029947(1990)09745240
Article copyright:
© Copyright 1990
American Mathematical Society
