Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A characterization of best $ \Phi $-approximants


Authors: D. Landers and L. Rogge
Journal: Trans. Amer. Math. Soc. 267 (1981), 259-264
MSC: Primary 46E30; Secondary 41A50
DOI: https://doi.org/10.1090/S0002-9947-1981-0621986-9
MathSciNet review: 621986
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ T$ be an operator from an Orlicz space $ {L_\Phi }$ into itself. It is shown in this paper that four algebraic conditions and one integration condition assure that $ T$ is the best $ \Phi $-approximator, given a suitable $ \sigma $-lattice.


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

  • [1] T. Ando, Contractive projections in $ {L_p}$-spaces, Pacific J. Math. 17 (1966), 391-405. MR 0192340 (33:566)
  • [2] T. Ando and I. Amemiya, Almost everywhere convergence of prediction sequence in $ {L_p}(1 < p < \infty )$, Z. Wahrsch. Verw. Gebiete 4 (1965), 113-120. MR 0189077 (32:6504)
  • [3] R. R. Bahadur, Measurable subspaces and subalgebras, Proc. Amer. Math. Soc. 6 (1955), 565-570. MR 0072446 (17:286c)
  • [4] R. E. Barlow, D. J. Bartholomew, J. M. Bremner and H. D. Brunk, Statistical inference under order restrictions, Wiley, New York, 1972. MR 0326887 (48:5229)
  • [5] H. D. Brunk, On an extension of the concept conditional expectation, Proc. Amer. Math. Soc. 14 (1963), 298-304. MR 0148090 (26:5599)
  • [6] -, Uniform inequalities for conditional $ p$-means given $ \sigma $-lattices, Ann. Probab. 3 (1975), 1025-1030. MR 0385945 (52:6804)
  • [7] R. G. Douglas, Contractive projections on an $ {L_1}$-space, Pacific J. Math. 15 (1965), 443-462. MR 0187087 (32:4541)
  • [8] R. L. Dykstra, A characterization of a conditional expectation with respect to a $ \sigma $-lattice, Ann. Math. Statist. 41 (1970), 698-701. MR 0258083 (41:2730)
  • [9] M. A. Krasnoselskii and Y. B. Rutickii, Convex functions and Orlicz spaces, Noordhoff, Groningen, 1961. MR 0126722 (23:A4016)
  • [10] D. Landers and L. Rogge, Characterization of $ p$-predictors, Proc. Amer. Math. Soc. 76 (1979), 307-309. MR 537095 (80f:47063)
  • [11] -, Best approximants in $ {L_\Phi }$-spaces, Z. Wahrsch. Verw. Gebiete 51 (1980), 215-237. MR 566317 (81c:41042)
  • [12] -, Isotonic approximation in $ {L_s}$, J. Approx. Theory (to appear).
  • [13] S. C. Moy, Characterization of conditional expectation as transformation on function spaces, Pacific J. Math. 4 (1954), 47-63. MR 0060750 (15:722a)
  • [14] J. Pfanzagl, Characterization of conditional expectations, Ann. Math. Statist. 38 (1967), 415-421. MR 0211430 (35:2310)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E30, 41A50

Retrieve articles in all journals with MSC: 46E30, 41A50


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0621986-9
Keywords: Best approximants, $ \sigma $-lattices, conditional expectations, characterization
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society