Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Orthogonality and nonlinear functionals


Authors: S. Gudder and D. Strawther
Journal: Bull. Amer. Math. Soc. 80 (1974), 946-950
MSC (1970): Primary 46B99, 46C05, 47H15; Secondary 46F05, 81A12
DOI: https://doi.org/10.1090/S0002-9904-1974-13589-5
MathSciNet review: 0352948
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. R. V. Chacon and N. Friedman, Additive functionals, Arch. Rational Mech. Anal. 18 (1965), 230-240. MR 30 #2329. MR 172103
  • 2. L. Drewnowski and W. Orlicz, On orthogonally additive functionals, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 883-888. MR 39 #6069. MR 244755
  • 3. N. Friedman and M. Katz, Additive functionals in L, Canad. J. Math. 18 (1966), 1264-1271. MR 34 #6510. MR 206692
  • 4. N. Friedman and M. Katz, A representation theorem for additive functionals, Arch. Rational Mech. Anal. 21 (1966), 49-57. MR 33 #245. MR 192018
  • 5. I. M. Gel'fand and N. Vilenkin, Generalized functions. Vol. 4: Some applications of harmonic analysis, Fizmatgiz, Moscow, 1961; English transl., Academic Press, New York, 1964. MR 26 #4173; 30 #4152. MR 435834
  • 6. J. R. Giles, Classes of semi-inner-product spaces, Trans. Amer. Math. Soc. 129 (1967), 436-446. MR 36 #663. MR 217574
  • 7. A. Gleason, Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6 (1957), 885-893. MR 20 #2609. MR 96113
  • 8. R. James, Orthogonality and linear functional in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265-292. MR 9, 42. MR 21241
  • 9. H. Leaderman, F. McCrackin and O. Nakada, Large longitudinal retarded elastic deformation of rubberlike network polymers. II. Applications of a general formulation of nonlinear responses, Trans. Soc. Rheology 7 (1963), 111-123.
  • 10. A. Martin and V. Mizel, A representation theorem for non-linear functionals, Arch. Rational Mech. Anal. 15 (1964), 353-367. MR 162131
  • 11. V. Mizel, Representation of nonlinear transformations on L, Bull. Amer. Math. Soc. 75 (1969), 164-168. MR 38 #4983. MR 236688
  • 12. V. Mizel and K. Sundaresan, Representation of additive and biadditive functionals, Arch. Rational Mech. Anal. 30 (1968), 102-126. MR 37 #3341. MR 227757
  • 13. R. Rivlin, Stress relaxation in elastic materials for varying deformation, Armstrong Cork Co., Technical Report, June 1954.
  • 14. K. Sundaresan, Additive functionals on Orlicz spaces, Studia Math. 32 (1968), 269-276. MR 40 #1765. MR 248513
  • 15. K. Sundaresan, Orthogonality and nonlinear functionals on Banach spaces, Proc. Amer. Math. Soc. 34 (1972), 187-190. MR 45 #925. MR 291835

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 46B99, 46C05, 47H15, 46F05, 81A12

Retrieve articles in all journals with MSC (1970): 46B99, 46C05, 47H15, 46F05, 81A12


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1974-13589-5

American Mathematical Society