Product shifts on $B(H)$
HTML articles powered by AMS MathViewer
- by P. J. Stacey PDF
- Proc. Amer. Math. Soc. 113 (1991), 955-963 Request permission
Abstract:
A shift on $B(H)$ is a $*$-endomorphism $\alpha$ for which ${ \cap _r}{\alpha ^r}(B(H)) = \mathbb {C}P$ for some projection $P$. The paper discusses some aspects of the classification of shifts on $B(H)$ up to conjugacy by $*$-automorphisms, with a focus on the shifts arising from an infinite tensor product decomposition of $H$.References
- R. J. Archbold, On the âflip-flopâ automorphism of $C^{\ast } (S_{1},\,S_{2})$, Quart. J. Math. Oxford Ser. (2) 30 (1979), no. 118, 129â132. MR 534827, DOI 10.1093/qmath/30.2.129
- William Arveson, Continuous analogues of Fock space, Mem. Amer. Math. Soc. 80 (1989), no. 409, iv+66. MR 987590, DOI 10.1090/memo/0409
- A. Guichardet, Produits tensoriels infinis et reprĂ©sentations des relations dâanticommutation, Ann. Sci. Ăcole Norm. Sup. (3) 83 (1966), 1â52 (French). MR 0205097, DOI 10.24033/asens.1146
- Paul Richard Halmos, A Hilbert space problem book, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 17, Springer-Verlag, New York-Berlin, 1982. MR 675952, DOI 10.1007/978-1-4684-9330-6 H. Hanche-Olsen and E. StĂžrmer, Jordan operator algebras, Pitman, 1984.
- J. von Neumann, On infinite direct products, Compositio Math. 6 (1939), 1â77. MR 1557013
- Robert T. Powers, An index theory for semigroups of $^*$-endomorphisms of ${\scr B}({\scr H})$ and type $\textrm {II}_1$ factors, Canad. J. Math. 40 (1988), no. 1, 86â114. MR 928215, DOI 10.4153/CJM-1988-004-3
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 955-963
- MSC: Primary 46L40; Secondary 46L55, 47A99
- DOI: https://doi.org/10.1090/S0002-9939-1991-1057945-6
- MathSciNet review: 1057945