Separately σ-additive and separately finitely additive complex functions on the Cartesian product of two algebras of sets are represented in terms of spectral measures and their finitely additive counterparts. Applications of the techniques include a bounded joint convergence theorem for bimeasure integration, characterizations of positive-definite bimeasures, and a theorem on decomposing a bimeasure into a linear combination of positive-definite ones.
@article{bwmeta1.element.bwnjournal-article-smv104i3p269bwm,
author = {Kari Ylinen},
title = {Representations of bimeasures},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {269-278},
zbl = {0809.28001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv104i3p269bwm}
}
Ylinen, Kari. Representations of bimeasures. Studia Mathematica, Tome 104 (1993) pp. 269-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i3p269bwm/
[00000] [1] D. K. Chang and M. M. Rao, Bimeasures and nonstationary processes, in: Real and Stochastic Analysis, M. M. Rao (ed.), Wiley, New York 1986, 7-118. | Zbl 0616.60009
[00001] [2] S. D. Chatterji, Orthogonally scattered dilation of Hilbert space valued set functions, in: Measure Theory (Proc. Conf. Oberwolfach 1981), Lecture Notes in Math. 945, Springer, Berlin 1982, 269-281. | Zbl 0489.28007
[00002] [3] E. Christensen and A. M. Sinclair, Representations of completely bounded multilinear operators, J. Funct. Anal. 72 (1987), 151-181. | Zbl 0622.46040
[00003] [4] N. Dunford and J. T. Schwartz, Linear Operators I: General Theory, Pure Appl. Math. 7, Interscience, New York 1958. | Zbl 0084.10402
[00004] [5] J. E. Gilbert, T. Ito and B. M. Schreiber, Bimeasure algebras on locally compact groups, J. Funct. Anal. 64 (1985), 134-162. | Zbl 0601.43001
[00005] [6] C. C. Graham and B. Schreiber, Bimeasure algebras on LCA groups, Pacific J. Math. 115 (1984), 91-127. | Zbl 0502.43005
[00006] [7] A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Math. São Paulo 8 (1956), 1-79. | Zbl 0074.32303
[00007] [8] P. R. Halmos, Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), 125-134.
[00008] [9] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, London 1967.
[00009] [10] S. Kaijser and A. M. Sinclair, Projective tensor products of C*-algebras, Math. Scand. 55 (1984), 161-187. | Zbl 0557.46036
[00010] [11] A. Makagon and H. Salehi, Spectral dilation of operator-valued measures and its application to infinite-dimensional harmonizable processes, Studia Math. 85 (1987), 257-297. | Zbl 0625.60042
[00011] [12] M. Takesaki, Theory of Operator Algebras I, Springer, New York 1979.
[00012] [13] K. Ylinen, On vector bimeasures, Ann. Mat. Pura Appl. (4) 117 (1978), 115-138. | Zbl 0399.46032
[00013] [14] K. Ylinen, Dilations of V-bounded stochastic processes indexed by a locally compact group, Proc. Amer. Math. Soc. 90 (1984), 378-380. | Zbl 0531.60014
[00014] [15] K. Ylinen, Noncommutative Fourier transforms of bounded bilinear forms and completely bounded multilinear operators, J. Funct. Anal. 79 (1988), 144-165. | Zbl 0663.46053
[00015] [16] K. Yosida and E. Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46-66. | Zbl 0046.05401