Controlling and supporting sets in operator algebras

Burnap, Charles; Lambert, Alan

doi:10.1090/S0002-9939-99-04830-3

Controlling and supporting sets in operator algebras
HTML articles powered by AMS MathViewer

by Charles Burnap and Alan Lambert PDF

Proc. Amer. Math. Soc. 127 (1999), 1357-1362 Request permission

Abstract:

Two properties of subspaces of Banach algebras are introduced. These are closely related to Mathieu’s concept of ultraprime Banach algebras. Special attention is paid to nested $C^*$ and $W^*$ algebras.

References

James A. Deddens, Another description of nest algebras, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977) Lecture Notes in Math., vol. 693, Springer, Berlin, 1978, pp. 77–86. MR 526534
Domingo A. Herrero, On iterated similarities of operators, Proc. Amer. Math. Soc. 72 (1978), no. 3, 519–520. MR 509246, DOI 10.1090/S0002-9939-1978-0509246-3
Domingo A. Herrero, A note on iterated similarities of operators, Rev. Un. Mat. Argentina 36 (1990), 138–145 (1992). MR 1265702
M. Mathieu, Applications of ultraprime Banach algebras in the theory of elementary operators, Ph.D. dissertation, Universität Tübingen, 1986.
Martin Mathieu, Spectral theory for multiplication operators on $C^{\ast }$-algebras, Proc. Roy. Irish Acad. Sect. A 83 (1983), no. 2, 231–249. MR 736499
Martin Mathieu (ed.), Elementary operators & applications, World Scientific Publishing Co., Inc., River Edge, NJ, 1992. In memory of Domingo A. Herrero. MR 1183935, DOI 10.1142/1610
Joseph G. Stampfli, On a question of Deddens, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977) Lecture Notes in Math., vol. 693, Springer, Berlin, 1978, pp. 169–173. MR 526546
B. Sz-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Scient. Math. (Szeged), 11 (1947), 152–157.
D. M. Topping, Lectures on von Neumann Algebras, Van Nostrand Reinhold Co., London 1971.
J. P. Williams, On a boundedness condition for operators with a singleton spectrum, Proc. Amer. Math. Soc. 78 (1980), no. 1, 30–32. MR 548078, DOI 10.1090/S0002-9939-1980-0548078-6