Representations of bimeasures

Kari Ylinen

Studia Mathematica (1993)

  • Volume: 104, Issue: 3, page 269-278
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Ylinen, Kari. "Representations of bimeasures." Studia Mathematica 104.3 (1993): 269-278. <http://eudml.org/doc/215975>.

@article{Ylinen1993,
abstract = {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.},
author = {Ylinen, Kari},
journal = {Studia Mathematica},
keywords = {representations; bimeasures; convergence theorem; bimeasure integration; positive-definite bimeasures},
language = {eng},
number = {3},
pages = {269-278},
title = {Representations of bimeasures},
url = {http://eudml.org/doc/215975},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Ylinen, Kari
TI - Representations of bimeasures
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 3
SP - 269
EP - 278
AB - 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.
LA - eng
KW - representations; bimeasures; convergence theorem; bimeasure integration; positive-definite bimeasures
UR - http://eudml.org/doc/215975
ER -

References

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  11. [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. Zbl0625.60042
  12. [12] M. Takesaki, Theory of Operator Algebras I, Springer, New York 1979. 
  13. [13] K. Ylinen, On vector bimeasures, Ann. Mat. Pura Appl. (4) 117 (1978), 115-138. Zbl0399.46032
  14. [14] K. Ylinen, Dilations of V-bounded stochastic processes indexed by a locally compact group, Proc. Amer. Math. Soc. 90 (1984), 378-380. Zbl0531.60014
  15. [15] K. Ylinen, Noncommutative Fourier transforms of bounded bilinear forms and completely bounded multilinear operators, J. Funct. Anal. 79 (1988), 144-165. Zbl0663.46053
  16. [16] K. Yosida and E. Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46-66. Zbl0046.05401

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