Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T00:45:23.867Z Has data issue: false hasContentIssue false
  • English
  • Français

The generalized Yosida–Hewitt theorem

Published online by Cambridge University Press:  24 October 2008

A. Basile ,
A. V. Bukhvalov  and
M. Ya. Yakubson
A. Basile
Affiliation:
Dipartimento di Matematica e Applicazioni, Complesso Monte S. Angelo, Università Federico II, Via Cintia, 80126 Napoli, Italy
A. V. Bukhvalov
Affiliation:
Department of Mathematics, St Petersburg University of Economics and Finance, Sadovaya Street 21, 191023 St Petersburg, Russia
M. Ya. Yakubson
Affiliation:
Department of Mathematical Analysis, St Petersburg Pedagogical University, St Petersburg, Russia
Get access Rights & Permissions [Opens in a new window]

Extract

The Yosida–Hewitt (YH, for short) theorem [YH] has many versions and generalizations in diverse settings, e.g. functionals on vector lattices and spaces of vector-valued functions, measures with values in Banach spaces, topological groups and vector lattices, etc. In this paper we derive a very general form of the YH theorem dealing with the much more general case of operators acting in vector lattices (VLs, for short) and Banach spaces (BSs, for short). A unified approach to all settings mentioned above may be founded on decompositions for operators in VLs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 3 , November 1994 , pp. 527 - 533
Copyright
Copyright © Cambridge Philosophical Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[AB]Aliprantis, C. D. and Burkinshaw, O.. Positive Operators (Academic Press, 1985).Google Scholar
[BL]Bukhvalov, A. V. and Lozanovskǐ, G. Ya.. On sets closed in measure in spaces of measurable functions. Trudy Moskov. Mat. Ob-va 34 (1977), 129–150; English transl. Trans. Moscow Math. Soc. (1978), issue 2, 127–150.Google Scholar
[D]Dodds, P. G.. o-Weakly compact mappings of Riesz spaces. Trans. Amer. Math. Soc. 214 (1975), 389–402.Google Scholar
[KVP]Kantorovich, L. V., Vulikh, B. Z. and Pinsker, A. G.. Functional Analysis in Partially Ordered Spaces (Gostekhizdat, Moscow-Leningrad, 1950), (Russian).Google Scholar
[Lo1]Lozanovskiĭ, G. Ya.. On localizable functionals in vector lattices. Theory of Functions, Fund. Anal., and Their Applications (Khar'kov) 19 (1974), 66–68 (Russian).Google Scholar
[Lo2]Lozanovskiĭ, G. Ya.. Supplement to the paper ‘Localizable functionals in vector lattices’. Zap. Nauchn. Sem. LOMI 56 (1976), 188–190; English transl. J. Soviet Math. 14 (1980), 1170–1173.Google Scholar
[LZ]Luxemburg, W. A. J. and Zaanen, A. C.. Riesz Spaces I (North-Holland 1971).Google Scholar
[T]Traynor, T.. The Lebesgue decomposition for group-valued additive set functions. Trans. Amer. Math. Soc. 220 (1976), 307–319.Google Scholar
[Ve]Veksler, A. I.. P′-points, P′-sets, P′-spaces. A new class of order-continuous measures and functionals. Dokl. Akad. Nauk SSSR 212 (1973), 789–792; English transl. Functional Anal. Appl. 14 (1973), 1445–1450.Google Scholar
[V]Vulikh, B. Z.. Introduction to the Theory of Partially Ordered Spaces (Fizmatgiz, Moscow, 1961; English transl. Noordhoff, 1967).Google Scholar
[YH]Yosida, K. and Hewitt, E.. Finitely additive measures. Trans. Amer. Math. Soc. 72 (1952), 46–66.Google Scholar
[Z]Zaanen, A. C.. Riesz Spaces II (North-Holland, 1983).Google Scholar