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
Additional Information
- Charles Burnap
- Affiliation: Department of Mathematics, The University of North Carolina at Charlotte, Charlotte, North Carolina 28223
- Email: caburnap@email.uncc.edu
- Alan Lambert
- Affiliation: Department of Mathematics, The University of North Carolina at Charlotte, Charlotte, North Carolina 28223
- Email: allamber@email.uncc.edu
- Received by editor(s): August 6, 1997
- Published electronically: January 28, 1999
- Communicated by: David R. Larson
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1357-1362
- MSC (1991): Primary 46L05, 46H20, 47B47
- DOI: https://doi.org/10.1090/S0002-9939-99-04830-3
- MathSciNet review: 1600112