Splittings of Banach spaces
induced by Clifford algebras
Authors:
N. L. Carothers, S. J. Dilworth and David Sobecki
Journal:
Proc. Amer. Math. Soc. 128 (2000), 1347-1356
MSC (1991):
Primary 46B20
DOI:
https://doi.org/10.1090/S0002-9939-99-05374-5
Published electronically:
October 18, 1999
MathSciNet review:
1670426
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be an infinite-dimensional Hilbert space of density character
. By representing
as a module over an appropriate Clifford algebra, it is proved that
possesses a family
of proper closed nonzero subspaces such that
Analogous results are proved for spaces and for
and
(
) when
is an arbitrary nonzero Banach space.
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- 2. Edwin Hewitt and Karl Stromberg, Real and Abstract Analysis, Springer-Verlag, New York, 1965. MR 32:5826
- 3. Serge Lang, Algebra, Addison-Wesley, Reading, MA, 1965. MR 33:5416
- 4. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math. Vol. 338, Springer-Verlag, Berlin-Heidelberg-New York, 1973. MR 55:3344
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Additional Information
N. L. Carothers
Affiliation:
Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43402
Email:
carother@math.bgsu.edu
S. J. Dilworth
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email:
dilworth@math.sc.edu
David Sobecki
Affiliation:
Department of Mathematics, Miami University, Hamilton, Ohio 45014
Email:
sobeckdm@muohio.edu
DOI:
https://doi.org/10.1090/S0002-9939-99-05374-5
Received by editor(s):
June 19, 1998
Published electronically:
October 18, 1999
Communicated by:
Dale Alspach
Article copyright:
© Copyright 2000
American Mathematical Society