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A factorization theorem in Banach lattices and its application to Lorentz spaces

Sholomo Reisner

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 1, page 239-255
  • ISSN: 0373-0956

Abstract

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p -convexity and q -concavity of a Banach lattice L are characterized by factorization of multiplication operators from L q into L p through L . This characterization is applied to calculate the concavity type of Lorentz spaces.

How to cite

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Reisner, Sholomo. "A factorization theorem in Banach lattices and its application to Lorentz spaces." Annales de l'institut Fourier 31.1 (1981): 239-255. <http://eudml.org/doc/74485>.

@article{Reisner1981,
abstract = {$p$-convexity and $q$-concavity of a Banach lattice $L$ are characterized by factorization of multiplication operators from $L_q$ into $L_p$ through $L$. This characterization is applied to calculate the concavity type of Lorentz spaces.},
author = {Reisner, Sholomo},
journal = {Annales de l'institut Fourier},
keywords = {p-convexity; q-concavity; Banach lattice; factorization of multiplication operators; concavity type of Lorentz spaces},
language = {eng},
number = {1},
pages = {239-255},
publisher = {Association des Annales de l'Institut Fourier},
title = {A factorization theorem in Banach lattices and its application to Lorentz spaces},
url = {http://eudml.org/doc/74485},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Reisner, Sholomo
TI - A factorization theorem in Banach lattices and its application to Lorentz spaces
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 1
SP - 239
EP - 255
AB - $p$-convexity and $q$-concavity of a Banach lattice $L$ are characterized by factorization of multiplication operators from $L_q$ into $L_p$ through $L$. This characterization is applied to calculate the concavity type of Lorentz spaces.
LA - eng
KW - p-convexity; q-concavity; Banach lattice; factorization of multiplication operators; concavity type of Lorentz spaces
UR - http://eudml.org/doc/74485
ER -

References

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  1. [1] Z. ALTSHULER, Uniform convexity in Lorentz sequence spaces, Israel J. Math., 20 (1975), 260-274. Zbl0309.46007MR52 #6378
  2. [2] A.P. CALDERON, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113-190. Zbl0204.13703MR29 #5097
  3. [3] T. FIGIEL, W.B. JOHNSON and L. TZAFRIRI, On Banach lattices and spaces having local unconditional structure, with applications to Lorentz function spaces, J. Approx. Th., 13 (1975), 395-412. Zbl0307.46007MR51 #3866
  4. [4] I. HALPERIN, Uniform convexity in function spaces, Canadian J. Math., 21 (1954), 195-204. Zbl0055.33702MR15,880b
  5. [5] R.E. JAMISON and W.H. RUCKLE, Factoring absolutely convergent series, Math. Ann., 227 (1976), 143-148. Zbl0319.40007MR55 #8747
  6. [6] J.L. KRIVINE, Théorèmes de factorisation dans les espaces réticulés, Séminaire Maurey-Schwartz, 1973-1974, Exp. 12-13. 
  7. [7] J. LINDENSTRAUSS and L. TZAFRIRI, Classical Banach spaces, parts I and II, Springer Verlag, 1979. Zbl0403.46022MR81c:46001
  8. [8] G.G. LORENTZ, On the theory of spaces Λ, Pacific J. Math., 1 (1951), 411-429. Zbl0043.11302MR13,470c
  9. [9] G.Y. LOZANOVSKII, On some Banach lattices, Siberian Math. J., 10 (1969), 419-430. Zbl0194.43302
  10. [10] G. PISIER, Some applications of the complex interpolation method to Banach lattices, J. D'Analyse Math., 35 (1979), 264-280. Zbl0427.46048MR80m:46020

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