Journal of Lie Theory, Vol. 10, No. 1, pp. 107-109 (2000)

Supplements to the papers entitled "On a Theorem of S. Banach" and "The separable representations of U(H)"

Karl-Hermann Neeb and Doug Pickrell

Fachbereich Mathematik
Technische Universitšt Darmstadt
Schlo\3gartenstra\3e 7
D-645289 Darmstadt, Germany
neeb@mathemtik.tu-darmstadt.de
and
Department of Mathematics
University of Arizona
Tucson AZ 85721-0001, USA
pickrell@ame2.math.arizona.edu

Abstract: We explain how the theorem of Banach discussed in [Ne97] can be generalized to target spaces which are not necessarily path connected. Moreover, we correct errors in the literature concerning the classification of separable unitary representations for the Banach Lie group {$U(H)$} [Pi88, Pi90].}

{\eightrm [Ne97] Neeb, K.-H., {\eightit On a Theorem of S. Banach}, Journal of Lie Theory 7 (1997), 293-300.

[Pi88] Pickrell, D., \eightit The Separable Representations of \eightrm U$(\cal H)$, Proc. Amer. Math. Soc. 102 (1988), 416-420. \smallskip

[Pi90] - , {\eightit Separable Representations for Automorphism Groups of Infinite Symmetric Spaces}, J. Funct. Anal. 90 (1990), 1-26.

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