Projectionless C*-algebras

Kaonga, Llolsten

doi:10.1090/S0002-9939-01-06059-2

Projectionless C*-algebras
HTML articles powered by AMS MathViewer

by Llolsten Kaonga PDF

Proc. Amer. Math. Soc. 130 (2002), 33-38 Request permission

Abstract:

We give a sufficient condition for a unital C*-algebra to have no nontrivial projections, and we apply this result to known examples and to free products. We also show how questions of existence of projections relate to the norm-connectedness of certain sets of operators.

References

Man Duen Choi, The full $C^{\ast }$-algebra of the free group on two generators, Pacific J. Math. 87 (1980), no. 1, 41–48. MR 590864
John B. Conway, The theory of subnormal operators, Mathematical Surveys and Monographs, vol. 36, American Mathematical Society, Providence, RI, 1991. MR 1112128, DOI 10.1090/surv/036
J. Froelich and H. Salas, The C*-algebra generated by a C*-universal operator, preprint.
Donald W. Hadwin, Nonseparable approximate equivalence, Trans. Amer. Math. Soc. 266 (1981), no. 1, 203–231. MR 613792, DOI 10.1090/S0002-9947-1981-0613792-6
D. W. Hadwin, L. Kaonga, and B. Mathes, Noncommutative continuous functions, preprint.
L. Kaonga, Decomposable functions and universal C*-algebras, Ph.D. Thesis, University of New Hampshire (1994).
Kevin McClanahan, $C^*$-algebras generated by elements of a unitary matrix, J. Funct. Anal. 107 (1992), no. 2, 439–457. MR 1172034, DOI 10.1016/0022-1236(92)90117-2
N. Christopher Phillips, Classifying algebras for the $K$-theory of $\sigma$-$C^*$-algebras, Canad. J. Math. 41 (1989), no. 6, 1021–1089. MR 1018451, DOI 10.4153/CJM-1989-046-2