×

Representation of additive functionals on vector-valued normed Köthe spaces. (English) Zbl 0431.46025


MSC:

46E40 Spaces of vector- and operator-valued functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] R. A. ALO AND A. DE KORVIN, Representation of Hammerstein operators by Nemytskii measures, J. Math. Anal. Appl., 52 (1975), 490-513. · Zbl 0336.46049
[2] J. BATT, Nonlinear integral operators on C(S, E), Studia Math., 48 (1973), 145-177. · Zbl 0242.47040
[3] L. DREWNOWSKI AND W. ORLICZ, On orthogonally additive functionals, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 16 (1968), 883-888. · Zbl 0172.42003
[4] L. DREWNOWSKI AND W. ORLICZ, On representation of orthogonally additive functional, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 17 (1969), 167-173. · Zbl 0174.46201
[5] L. DREWNOWSKI AND W. ORLICZ, Continuity and representation of orthogonally additive functionals, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., IT (1969), 647-653. · Zbl 0198.19302
[6] N. A. FRIEDMAN AND M. KATZ, Additive functionals on Lp spaces, Canad. J. Math., 18 (1966), 1264-1271. · Zbl 0145.38903
[7] N. E. GRETSKY AND J. J. UHL, JR., Bounded linear operators on Banach function spaces of vector-valued functions, Trans. Amer. Math. Soc, 167 (1972), 263-277. · Zbl 0238.46038
[8] F. HIAI AND H. UMEGAKI, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal., 7 (1977), 149-182. · Zbl 0368.60006
[9] C. J. HIMMELBERG, Measurable relations, Fund. Math., 87 (1975), 53-72. · Zbl 0296.28003
[10] M. A. KRASNOSEL’SKII, Topological Methods in the Theory of Nonlinear Integral Equations, translated by J. Burlak, Macmillan, New York, 1964. · Zbl 0111.30303
[11] A. D. MARTIN AND V. J. MIZEL, A representation theorem for certain nonlinear functionals, Arch. Rational Mech. Anal., 15 (1964), 353-367. · Zbl 0131.33001
[12] V. J. MIZEL, Characterization of non-linear transformations possessing kernels, Canad. J. Math., 22 (1970), 449-471. · Zbl 0203.14302
[13] V. J. MIZEL AND K. SUNDARESAN, Representation of additive and biadditive functionals, Arch. Rational Mech. Anal., 30 (1968), 102-126. · Zbl 0165.49903
[14] V. J. MIZEL AND K. SUNDARESAN, Additive functionals on spaces with nonabsolutely-continuous norm, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 18 (1970), 385-389. · Zbl 0195.42503
[15] V. J. MIZEL AND K. SUNDARESAN, Representation of vector valued nonlinear functions, Trans. Amer. Math. Soc, 159 (1971), 111-127. · Zbl 0235.46070
[16] J. A. PALAGALLO, A representation of additive functionals on L^-spaces, 0<p<l, Pacific J. Math., 66 (1976), 221-234. Zentralblatt MATH: · Zbl 0342.28003
[17] M. -F. SAINTE-BEUVE, On the extension of von Neumann-Aumann’s theorem, J. Functional Anal., 17 (1974), 112-129. · Zbl 0286.28005
[18] C. STEGALL, The Radon-Nikodym property in conjugate Banach spaces, Trans. Amer. Math. Soc, 206 (1975), 213-223. · Zbl 0318.46056
[19] K. SUNDARESAN, Additive functionals on Orlicz spaces, Studia Math., 32 (1969), 269-276. · Zbl 0194.16602
[20] D. H. WAGNER, Survey of measurable selection theorems, SIAM J. Control and Optimization, 15 (1977), 859-903. · Zbl 0407.28006
[21] W. A. WOYCZYNSKI, Additive functions on Orlicz spaces, Colloq. Math., 19 (1968), 319-326. · Zbl 0183.13702
[22] A. C. ZAANEN, Integration, revised ed., North-Holland, Amsterdam, 1967. · Zbl 0175.05002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.