Continuous extensions of spectral measures

S. Okada; W. Ricker

Colloquium Mathematicae (1996)

  • Volume: 71, Issue: 1, page 115-132
  • ISSN: 0010-1354

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Okada, S., and Ricker, W.. "Continuous extensions of spectral measures." Colloquium Mathematicae 71.1 (1996): 115-132. <http://eudml.org/doc/210417>.

@article{Okada1996,
author = {Okada, S., Ricker, W.},
journal = {Colloquium Mathematicae},
keywords = {extended measure; integrability; spectral measure; multiplicative operator-valued measure; completion; quasicompletion},
language = {eng},
number = {1},
pages = {115-132},
title = {Continuous extensions of spectral measures},
url = {http://eudml.org/doc/210417},
volume = {71},
year = {1996},
}

TY - JOUR
AU - Okada, S.
AU - Ricker, W.
TI - Continuous extensions of spectral measures
JO - Colloquium Mathematicae
PY - 1996
VL - 71
IS - 1
SP - 115
EP - 132
LA - eng
KW - extended measure; integrability; spectral measure; multiplicative operator-valued measure; completion; quasicompletion
UR - http://eudml.org/doc/210417
ER -

References

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  1. [1] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977. 
  2. [2] P. G. Dodds and and B. de Pagter, Orthomorphisms and Boolean algebras of projections, Math. Z. 187 (1984), 361-381. Zbl0538.46009
  3. [3] P. G. Dodds and W. J. Ricker, Spectral measures and the Bade reflexivity theorem, J. Funct. Anal. 61 (1985), 136-163. Zbl0577.46043
  4. [4] N. Dunford and J. T. Schwartz, Linear Operators I: General Theory, Wiley-Interscience, New York, 1958. Zbl0084.10402
  5. [5] N. Dunford and J. T. Schwartz, Linear Operators III: Spectral Operators, Wiley-Interscience, New York, 1972. Zbl0128.34803
  6. [6] I. Kluvánek and G. Knowles, Vector Measures and Control Systems, North-Holland, Amsterdam, 1975. Zbl0316.46043
  7. [7] G. Köthe, Topological Vector Spaces I, Grundlehren Math. Wiss. 159, Springer, Heidelberg, 1969. Zbl0179.17001
  8. [8] G. Köthe, Topological Vector Spaces II, Grundlehren Math. Wiss. 237, Springer, New York, 1979. Zbl0417.46001
  9. [9] D. R. Lewis, Integration with respect to vector measures, Pacific J. Math. 33 (1970), 157-165. Zbl0195.14303
  10. [10] S. Okada and W. J. Ricker, Spectral measures which fail to be equicontinuous, Period. Math. Hungar. 28 (1994), 55-61. Zbl0822.46055
  11. [11] S. Okada and W. J. Ricker, Vector measures and integration in non-complete spaces, Arch. Math. (Basel) 63 (1994), 344-353. Zbl0822.46056
  12. [12] S. Okada and W. J. Ricker, The range of the integration map of a vector measure, ibid. 64 (1995), 512-522. Zbl0832.28014
  13. [13] E. G. Ostling and A. Wilansky, Locally convex topologies and the convex compactness property, Proc. Cambridge Philos. Soc. 75 (1974), 45-50. Zbl0277.46002
  14. [14] W. J. Ricker, Closed spectral measures in Fréchet spaces, Internat. J. Math. Math. Sci. 7 (1984), 15-21. Zbl0577.46044
  15. [15] W. J. Ricker, Remarks on completeness in spaces of linear operators, Bull. Austral. Math. Soc. 34 (1986), 25-35. Zbl0621.46004
  16. [16] W. J. Ricker, Completeness of the L 1 -space of closed vector measures, Proc. Edinburgh Math. Soc. 33 (1990), 71-78. Zbl0668.46019
  17. [17] W. J. Ricker, Uniformly closed algebras generated by Boolean algebras of projections in locally convex spaces, Canad. J. Math. 34 (1987), 1123-1146. Zbl0627.47024
  18. [18] W. J. Ricker and H. H. Schaefer, The uniformly closed algebra generated by a complete Boolean algebra of projections, Math. Z. 201 (1989), 429-439. Zbl0655.47038
  19. [19] B. Walsh, Structure of spectral measures on locally convex spaces, Trans. Amer. Math. Soc. 120 (1965), 295-326. Zbl0138.38501

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