The uniform zero-two law for positive operators in Banach lattices

Michael Lin

Studia Mathematica (1998)

  • Volume: 131, Issue: 2, page 149-153
  • ISSN: 0039-3223

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Lin, Michael. "The uniform zero-two law for positive operators in Banach lattices." Studia Mathematica 131.2 (1998): 149-153. <http://eudml.org/doc/216571>.

@article{Lin1998,
abstract = {},
author = {Lin, Michael},
journal = {Studia Mathematica},
keywords = {zero-two law; positive power-bounded operators; Banach lattice},
language = {eng},
number = {2},
pages = {149-153},
title = {The uniform zero-two law for positive operators in Banach lattices},
url = {http://eudml.org/doc/216571},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Lin, Michael
TI - The uniform zero-two law for positive operators in Banach lattices
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 2
SP - 149
EP - 153
AB -
LA - eng
KW - zero-two law; positive power-bounded operators; Banach lattice
UR - http://eudml.org/doc/216571
ER -

References

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  1. [AR] G. R. Allan and T. J. Ransford, Power-dominated elements in Banach algebras, Studia Math. 94 (1989), 63-79. Zbl0705.46021
  2. [B] D. Berend, A note on the L p analogue of the “zero-two” law, Proc. Amer. Math. Soc. 114 (1992), 95-97. Zbl0754.47023
  3. [F] S. R. Foguel, More on the "zero-two" law, ibid. 61 (1976), 262-264. 
  4. [FWe] S. R. Foguel and B. Weiss, On convex power series of a conservative Markov operator, ibid. 38 (1973), 325-330. Zbl0268.47014
  5. [KT] Y. Katznelson and L. Tzafriri, On power bounded operators, J. Funct. Anal. 68 (1986), 312-328. Zbl0611.47005
  6. [M] J. Martinez, A representation lattice isomorphism for the peripheral spectrum, Proc. Amer. Math. Soc. 119 (1993), 489-492. Zbl0805.47031
  7. [OSu] D. Ornstein and L. Sucheston, An operator theorem on L 1 convergence to zero with applications to Markov kernels, Ann. Math. Statist. 41 (1970), 1631-1639. Zbl0284.60068
  8. [S1] H. Schaefer, Banach Lattices and Positive Operators, Springer, Berlin, 1974. Zbl0296.47023
  9. [S2] H. Schaefer, The zero-two law for positive contractions is valid in all Banach lattices, Israel J. Math. 59 (1987), 241-244. Zbl0657.47041
  10. [Sc] A. Schep, A remark on the uniform zero-two law for positive contractions, Arch. Math. (Basel) 53 (1989), 493-496. Zbl0702.47019
  11. [W1] R. Wittmann, Analogues of the zero-two law for positive contractions in L p and C(X), Israel J. Math. 59 (1987), 8-28. Zbl0654.46034
  12. [W2]] R. Wittmann, Ein starkes “Null-Zwei"-Gesetz in L p , Math. Z. 197 (1988), 223-229. 
  13. [Z1] R. Zaharopol, The modulus of a regular operator and the “zero-two” law in L p -spaces (1 < p < ∞, p ≠ 2), J. Funct. Anal. 68 (1986), 300-312. Zbl0613.47038
  14. [Z2] R. Zaharopol, Uniform monotonicity of norms and the strong "zero-two" law, J. Math. Anal. Appl. 139 (1989), 217-225. Zbl0688.47014
  15. [Ze] J. Zemánek, On the Gelfand-Hille theorems, in: Functional Analysis and Operator Theory, Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., 1994, 369-385. Zbl0822.47005

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