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Controlling and supporting sets in operator algebras
Author(s):
Charles
Burnap;
Alan
Lambert
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1357-1362.
MSC (1991):
Primary 46L05, 46H20, 47B47
Posted:
January 28, 1999
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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  and  algebras.
References:
- [D]
- J. A. Deddens, Another Description of Nests, Hilbert Space Operators, Proceedings, Long Beach, California, 1977. Lect. Notes Math. 693, Springer-Verlag, New York, 1978, 77-86. MR 80f:47033
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- D. A. Herrero, On iterated similarities of operators, Proc. Amer. Math. Soc. 72 (1978), 519-520. MR 80e:47014
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- D. A. Herrero, A note on iterated similarities of operators, Revista de la Unión Matemática Argentina 36 (1990), 138-145. MR 94k:47029
- [M1]
- M. Mathieu, Applications of ultraprime Banach algebras in the theory of elementary operators, Ph.D. dissertation, Universität Tübingen, 1986.
- [M2]
- -, Spectral theory for multiplication operators on
 -algebras, Proc. Royal Irish Acad. 83A (1983), 231-249. MR 85m:46055 - [M3]
- -, Ed., Elementary Operators and Applications, World Scientific, River Edge, N.J., 1992. MR 93e:47001
- [S]
- J. G. Stampfli, On a Question of Deddens, Hilbert Space Operators, Proceedings, Long Beach, California, 1977. Lecture Notes Math. 693, Springer-Verlag, New York, 1978, 169-173. MR 80f:47034
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- B. Sz-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Scient. Math. (Szeged), 11 (1947), 152-157.
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- D. M. Topping, Lectures on von Neumann Algebras, Van Nostrand Reinhold Co., London 1971.
- [W]
- J. P. Williams, On a boundedness condition for operators with a singleton spectrum, Proc. Amer. Math. Soc. 78 (1980), 30-32. MR 81k:47008
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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
DOI:
10.1090/S0002-9939-99-04830-3
PII:
S 0002-9939(99)04830-3
Received by editor(s):
August 6, 1997
Posted:
January 28, 1999
Communicated by:
David R. Larson
Copyright of article:
Copyright
1999,
American Mathematical Society
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