Extension theorems for nonlinear disjointly additive functionals and operators on Lebesgue spaces, with applications

Authors: Moshe Marcus and Victor J. Mizel
Journal: Bull. Amer. Math. Soc. 82 (1976), 115-117
MSC (1970): Primary 46E35, 46G99; Secondary 28A15
DOI: https://doi.org/10.1090/S0002-9904-1976-13982-1
Erratum, Volume 82: Bull. Amer. Math. Soc., Volume 82, Number 2 (1976), 353--353
MathSciNet review: 0402485
Full-text PDF Free Access

L. Drewnowski and W. Orlicz, Continuity and representation of orthogonally additive functionals, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 17 (1969), 647–653 (English, with Russian summary). MR 256147
J. F. C. Kingman and A. P. Robertson, On a theorem of Lyapunov, J. London Math. Soc. 43 (1968), 347–351. MR 224768, DOI https://doi.org/10.1112/jlms/s1-43.1.347

3. I. Kluvanek, Lectures on vector measures, Lecture notes, Van Nostrand Mathematical Studies (to appear).

M. A. Krasnosel′skiĭ, P. P. Zabreĭko, E. I. Pustyl′nik, and P. E. Sobolevskiĭ, Integral′nye operatory v prostranstvakh summiruemykh funktsiĭ, Izdat. “Nauka”, Moscow, 1966 (Russian). MR 0206751

5. M. Marcus and V. J. Mizel, Representation theorems for non-linear disjointly additive functionals on Sobolev spaces (to appear).

Victor J. Mizel, Characterization of non-linear transformations possessing kernels, Canadian J. Math. 22 (1970), 449–471. MR 262890, DOI https://doi.org/10.4153/CJM-1970-053-3
Victor J. Mizel and K. Sundaresan, Representation of vector valued nonlinear functions, Trans. Amer. Math. Soc. 159 (1971), 111–127. MR 279647, DOI https://doi.org/10.1090/S0002-9947-1971-0279647-8