Representations of bimeasures

• Autorzy: Kari Ylinen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 28A10: Real- or complex-valued set functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 104
• Numer: 3
• Strony: 269-278

Daty

wydano

1993

otrzymano

1992-05-13

poprawiono

1992-11-25

Twórcy

autor

Kari Ylinen

• Department of Mathematics, University of Turku, SF-20500 Turku, Finland

Bibliografia

• [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.
• [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.
• [3] E. Christensen and A. M. Sinclair, Representations of completely bounded multilinear operators, J. Funct. Anal. 72 (1987), 151-181.
• [4] N. Dunford and J. T. Schwartz, Linear Operators I: General Theory, Pure Appl. Math. 7, Interscience, New York 1958.
• [5] J. E. Gilbert, T. Ito and B. M. Schreiber, Bimeasure algebras on locally compact groups, J. Funct. Anal. 64 (1985), 134-162.
• [6] C. C. Graham and B. Schreiber, Bimeasure algebras on LCA groups, Pacific J. Math. 115 (1984), 91-127.
• [7] A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Math. São Paulo 8 (1956), 1-79.
• [8] P. R. Halmos, Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), 125-134.
• [9] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, London 1967.
• [10] S. Kaijser and A. M. Sinclair, Projective tensor products of C*-algebras, Math. Scand. 55 (1984), 161-187.
• [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.
• [12] M. Takesaki, Theory of Operator Algebras I, Springer, New York 1979.
• [13] K. Ylinen, On vector bimeasures, Ann. Mat. Pura Appl. (4) 117 (1978), 115-138.
• [14] K. Ylinen, Dilations of V-bounded stochastic processes indexed by a locally compact group, Proc. Amer. Math. Soc. 90 (1984), 378-380.
• [15] K. Ylinen, Noncommutative Fourier transforms of bounded bilinear forms and completely bounded multilinear operators, J. Funct. Anal. 79 (1988), 144-165.
• [16] K. Yosida and E. Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46-66.