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Projections in Spaces of Bimeasures

Published online by Cambridge University Press:  20 November 2018

Colin C. Graham  and
Bertram M. Schreiber
Colin C. Graham
Affiliation:
Department of Mathematics, University of British Columbia Vancouver, B.C. V6T 1Y4
Bertram M. Schreiber
Affiliation:
Department of Mathematics, Northwestern University Evanston, IL 60201
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Abstract

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Let X and Y be metrizable compact spaces and μ and v be nonzero continuous measures on X and Y, respectively. Then there is no bounded operator from the space of bimeasures BM(X, Y) onto the closed subspace of BM(X, Y) generated by L1 (μ X v); in particular, if X and Fare nondiscrete locally compact groups, then there is no bounded projection from BM(X, Y) onto the closed subspace of BM(X, Y) generated by L1(X X Y).

Keywords

43A2546J10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 19 - 25
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Bessaga, C. and Pefczynski, A., On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), pp. 151–164.Google Scholar
2. Gilbert, J. E., Ito, T. and Schreiber, B. M., Bimeasure algebras on locally compact groups, J. Functional Anal. 64 (1985), pp. 134–162.Google Scholar
3. Graham, C. C. and McGehee, O. C., Essays in commutative harmonic analysis, Grundl. der Math. Wissen., No. 238, Springer-Verlag, Berlin-New York, 1979.Google Scholar
4. Graham, C. C. and Schreiber, B. M., Bimeasure algebras on LCA groups, Pacific J. Math. 115 (1984), pp. 91–127.Google Scholar
5. Kelley, J. L., General Topology, van Nostrand, Princeton, 1955.Google Scholar
6. Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces, Lecture Notes in Math., No. 338, Springer-Verlag, Berlin-New York, 1973.Google Scholar
7. Saeki, S., Tensor products of C(X)-spaces and their conjugate spaces, J. Math. Soc. Japan 28 (1976), pp. 33–47.Google Scholar
8. Ylinen, K., Fourier transforms of noncommutative analogues of vector measures and bimeasures with applications to stochastic processes, Ann. Acad. Sci. Fenn., Ser A. I 1 (1975), pp. 355–385.Google Scholar