24
Views
0
CrossRef citations to date
0
Altmetric
Research articles

Strict topologies and spectral measures

Pages 675-695 | Received 17 Dec 2018, Published online: 17 Apr 2019

References

  • Y.A. Abramovich, E.L. Arenson and A.K. Kitover, Banach C(K)-modules and operators preserving disjointness, Pitman Research Notes in Mathematics Series, Vol. 277, Longman Scientific & Technical, Harlow, Essex, 1992.
  • E. Berkson and H.R. Dowson, Prespectral operators, Illinois J. Math. 13 (1969), 291–315. doi: 10.1215/ijm/1334250792
  • R.C. Buck, Bounded contiuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95–104. doi: 10.1307/mmj/1028998054
  • A. Cochran, Topological algebras and Mackey topologies, Proc. Amer. Math. Soc. 30(1) (1971), 115–119. doi: 10.1090/S0002-9939-1971-0291807-4
  • A. Cochran, Representation of A-convex algebras, Proc. Amer. Math. Soc. 41(2) (1973), 473–479.
  • A.C. Cochran, R. Keown and C.R. Wiliams, On a class of topological algebras, Pacific J. Math. 34(1) (1970), 17–25. doi: 10.2140/pjm.1970.34.17
  • J.B. Conway, The strict topology and compactness in the space of measures, II, Trans. Amer. Math. Soc. 126 (1967), 474–486. doi: 10.1090/S0002-9947-1967-0206685-2
  • J.B. Conway, A Course in Functional Analysis, Graduate Texts in Mathematics, Vol. 96, 2nd edition, Springer-Verlag, New York/Berlin/Heidelberg/Tokyo, 1990.
  • J.B. Cooper, The strict topology and spaces with mixed topologies, Proc. Amer. Math. Soc. 30(3) (1971), 583–592. doi: 10.1090/S0002-9939-1971-0284789-2
  • J. Diestel and J.J. Uhl, Vector Measures, Amer. Math. Soc., Math. Surveys, Vol. 15, AMS, Providence, RI, 1977.
  • N. Dunford, Spectral homomorphisms, Pacific J. Math. 4 (1954), 321–354. doi: 10.2140/pjm.1954.4.321
  • N. Dunford and J.T. Schwartz, Linear Operators III: Spectral Operators, Wiley-Interscience, New York, 1971.
  • L. Drewnowski, Topological rings of sets, continuous sets of functions, integration, II, Bull. Acad. Polon. Sci. Math. Astronom. Phys. 20 (1972), 277–286.
  • R.E. Edwards, Functional Analysis, Theory and Applications, Holt, Rinehart and Winston, New York, 1965.
  • R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
  • D. Fremlin, D.J.H. Garling and R.G. Haydon, Bounded measures on topological spaces, Proc. London Math. Soc. 25(3) (1972), 115–136. doi: 10.1112/plms/s3-25.1.115
  • R. Giles, A generalization of the strict topology, Trans. Amer. Math. Soc. 161 (1971), 467–474. doi: 10.1090/S0002-9947-1971-0282206-4
  • J. Hoffmann-Jörgënsen, Vector measures, Math. Scand. 28 (1971), 5–32. doi: 10.7146/math.scand.a-11003
  • J. Hoffmann-Jörgënsen, A generalization of the strict topology, Math. Scand. 30 (1972), 313–323. doi: 10.7146/math.scand.a-11087
  • S.S. Khurana, A topology associated with vector measures, J. Indian Math. Soc. 45 (1981), 167–179.
  • S.S. Khurana, Strict topologies as topological algebras, Czechoslovak Math. J. 51 (126) (2001), 433–437. doi: 10.1023/A:1013794801609
  • G. Köthe, Topological Vector Spaces I, Grundlehren Math. Wiss. No. 159, 2nd edition, Springer-Verlag, Berlin/Heidelberg, 1983. doi: 10.1007/978-3-642-64988-2
  • C. McArthur, On the theorem of Orlicz and Pettis, Pacific J. Math. 22(2) (1967), 297–302. doi: 10.2140/pjm.1967.22.297
  • S. Mitter and S.K. Young, Integration with respect to operator-valued measures with applications to quantum estimation theory, Ann. Mat. Pura Appl. 137(4) (1984), 1–39. doi: 10.1007/BF01789387
  • W.A. Luxemburg, Banach function spaces, Thesis Delft, Assen, 1955.
  • W.A. Luxemburg and A.C. Zaanen, Compactness of integral operators in Banach function spaces, Math. Annalen 149 (1963), 150–180. doi: 10.1007/BF01349240
  • M. Nowak, Integral representation of continuous operators with respect to strict topologies, Results in Math. 72 (2017) 843–863. doi: 10.1007/s00025-017-0678-4
  • M. Nowak, Spectral homomorphisms on a locally convex algebra Cb(X), Indag. Math. 28 (2017), 1157–1164. doi: 10.1016/j.indag.2017.08.006
  • B. de Pagter and W.J. Ricker, C(K)-representations and R-boundedness, J. London Math. Soc. 76(2) (2007), 498–512. doi: 10.1112/jlms/jdm072
  • W.J. Ricker, Operator algebras generated by commuting projections: a vector measure approach, Lecture Notes in Mathematics, Vol. 1711, Springer, Berlin, 1999. doi: 10.1007/BFb0096184
  • H.H. Schaefer, Topological Vector Spaces, Springer-Verlag, New York/Heidelberg/Berlin, 1971. doi: 10.1007/978-1-4684-9928-5
  • J. Schmets and J. Zafarani, Strict topologies and (gDF)-spaces, Arch. Math. 49 (1987), 227–231. doi: 10.1007/BF01271662
  • F. D. Sentilles, Bounded continuous functions on a completely regular space, Trans. Amer. Math. Soc. 168 (1972), 311–336. doi: 10.1090/S0002-9947-1972-0295065-1
  • A. Shuchat, Vector measures and the spectral theorem, In: Vector and Operator Measures and Applications, (Proc. Sympos. Alta, Utah, 1972), pp. 339–341, Academic Press, New York, 1973. doi: 10.1016/B978-0-12-702450-9.50036-1
  • A. Shuchat, Vector measures and scalar operators on locally convex spaces, Mich. Math. J. 24 (1977), 308–310.
  • A. Shuchat, Spectral measures and homomomorphisms, Rev. Roum. Math. Pures et Appl. 23(6) (1978), 939–945.
  • R. Wheeler, A servey of Baire measures and strict topologies, Expo. Math. 2 (1983), 97–190.
  • A. Wiweger, Linear spaces with mixed topology, Studia Math. 20 (1961), 47–68. doi: 10.4064/sm-20-1-47-68

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.