Boundary representations on -algebras with matrix units
Author:
Alan Hopenwasser
Journal:
Trans. Amer. Math. Soc. 177 (1973), 483-490
MSC:
Primary 46L05
DOI:
https://doi.org/10.1090/S0002-9947-1973-0322522-2
MathSciNet review:
0322522
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a
-algebra with unit, let
be a linear subspace of
which contains the natural set of matrix units and which generates
as a
-algebra. Let
be the subset of
consisting of entries of matrices in
. Then the boundary representations of
relative to
are parametrized by the boundary representations of
relative to
. Also, a nontrivial example is given of a subalgebra of a
-algebra which possesses exactly one boundary representation.
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William B. Arveson, Subalgebras of
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- [2]
-, Subalgebras of
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- [3] Robert R. Phelps, Lectures on Choquet's theorem, Van Nostrand, Princeton, N. J., 1966. MR 33 #1690. MR 0193470 (33:1690)
- [4] Donald Sarason, On spectral sets having connected complement, Acta Sci. Math. (Szeged) 26 (1965), 289-299. MR 32 #6229. MR 0188797 (32:6229)
- [5]
W. F. Stinespring, Positive functions on
-algebras, Proc. Amer. Math. Soc. 6 (1955), 211-216. MR 16, 1033. MR 0069403 (16:1033b)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1973-0322522-2
Keywords:
-algebra,
boundary representation,
matrix units,
Choquet boundary
Article copyright:
© Copyright 1973
American Mathematical Society