The Russo-Dye theorem in nest algebras

Davidson, Kenneth

doi:10.1090/S0002-9939-98-04538-9

The Russo-Dye theorem in nest algebras
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by Kenneth R. Davidson PDF

Proc. Amer. Math. Soc. 126 (1998), 3055-3059 Request permission

Abstract:

It is shown that the convex hull of the unitary elements of a nest algebra contains the whole unit ball if and only if both $0_+$ and $I_-^\perp$ are either zero or infinite rank.

References

M. Anoussis and E. G. Katsoulis, A non-selfadjoint Russo-Dye theorem, Math. Ann. 304 (1996), no. 4, 685–699. MR 1380450, DOI 10.1007/BF01446314
Kenneth R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. Triangular forms for operator algebras on Hilbert space. MR 972978
Richard V. Kadison and Gert K. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), no. 2, 249–266. MR 832356, DOI 10.7146/math.scand.a-12116
David R. Larson, Nest algebras and similarity transformations, Ann. of Math. (2) 121 (1985), no. 3, 409–427. MR 794368, DOI 10.2307/1971180
R. L. Moore and T. T. Trent, Extreme points of certain operator algebras, Indiana Univ. Math. J. 36 (1987), no. 3, 645–650. MR 905616, DOI 10.1512/iumj.1987.36.36036
B. Russo and H. A. Dye, A note on unitary operators in $C^{\ast }$-algebras, Duke Math. J. 33 (1966), 413–416. MR 193530, DOI 10.1215/S0012-7094-66-03346-1