Contractive projections on the fixed point set of L ∞ contractions

Michael Lin; Robert Sine

Colloquium Mathematicae (1991)

  • Volume: 62, Issue: 1, page 91-96
  • ISSN: 0010-1354

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Lin, Michael, and Sine, Robert. "Contractive projections on the fixed point set of $L_∞$ contractions." Colloquium Mathematicae 62.1 (1991): 91-96. <http://eudml.org/doc/210104>.

@article{Lin1991,
author = {Lin, Michael, Sine, Robert},
journal = {Colloquium Mathematicae},
keywords = {$L_∞$; projection; contraction; binary ball intersection; ergodic; positive operator; fixed point; commutative semigroup of linear contractions; common fixed points; existence of contractive projections},
language = {eng},
number = {1},
pages = {91-96},
title = {Contractive projections on the fixed point set of $L_∞$ contractions},
url = {http://eudml.org/doc/210104},
volume = {62},
year = {1991},
}

TY - JOUR
AU - Lin, Michael
AU - Sine, Robert
TI - Contractive projections on the fixed point set of $L_∞$ contractions
JO - Colloquium Mathematicae
PY - 1991
VL - 62
IS - 1
SP - 91
EP - 96
LA - eng
KW - $L_∞$; projection; contraction; binary ball intersection; ergodic; positive operator; fixed point; commutative semigroup of linear contractions; common fixed points; existence of contractive projections
UR - http://eudml.org/doc/210104
ER -

References

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  3. [Br] R. E. Bruck, Jr., A common fixed point theorem for a commuting family of nonexpansive mappings, Pacific J. Math. 53 (1974), 59-71. 
  4. [Ka] S. Kakutani, Some characterizations of Euclidean space, Japan. J. Math. 16 (1939), 93-97. Zbl0022.15001
  5. [Kr] U. Krengel, Ergodic Theorems, de Gruyter Stud. Math. 6, Berlin 1985. 
  6. [La] H. E. Lacey, The Isometric Theory of Classical Banach Spaces, Springer, Berlin 1974. Zbl0285.46024
  7. [LS] M. Lin and R. Sine, On the fixed point set of nonexpansive order preserving maps, Math. Z. 203 (1990), 227-234. Zbl0662.47030
  8. [LT] J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1971), 263-269. Zbl0211.16301
  9. [L1] S. P. Lloyd, An adjoint ergodic theorem, in: Ergodic Theory, F. B. Wright (ed.), Academic Press, 1963, 195-201. 
  10. [L2] S. P. Lloyd, Feller boundary induced by a transition operator, Pacific J. Math. 27 (1968), 547-566. Zbl0167.44501
  11. [L3] S. P. Lloyd, Poisson-Martin representation of excessive functions, unpublished manu- script. 
  12. [Si] R. C. Sine, On nonlinear contraction semigroups in sup norm spaces, Nonlinear Anal. 3 (1979), 885-890. Zbl0423.47035
  13. [So] P. Soardi, Existence of fixed point of nonexpansive mappings in certain Banach lattices, Proc. Amer. Math. Soc. 73 (1979), 25-29. Zbl0371.47048

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