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

Annales de l'institut Fourier (1981)

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

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topReisner, 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

top- [1] Z. ALTSHULER, Uniform convexity in Lorentz sequence spaces, Israel J. Math., 20 (1975), 260-274. Zbl0309.46007MR52 #6378
- [2] A.P. CALDERON, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113-190. Zbl0204.13703MR29 #5097
- [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] I. HALPERIN, Uniform convexity in function spaces, Canadian J. Math., 21 (1954), 195-204. Zbl0055.33702MR15,880b
- [5] R.E. JAMISON and W.H. RUCKLE, Factoring absolutely convergent series, Math. Ann., 227 (1976), 143-148. Zbl0319.40007MR55 #8747
- [6] J.L. KRIVINE, Théorèmes de factorisation dans les espaces réticulés, Séminaire Maurey-Schwartz, 1973-1974, Exp. 12-13.
- [7] J. LINDENSTRAUSS and L. TZAFRIRI, Classical Banach spaces, parts I and II, Springer Verlag, 1979. Zbl0403.46022MR81c:46001
- [8] G.G. LORENTZ, On the theory of spaces Λ, Pacific J. Math., 1 (1951), 411-429. Zbl0043.11302MR13,470c
- [9] G.Y. LOZANOVSKII, On some Banach lattices, Siberian Math. J., 10 (1969), 419-430. Zbl0194.43302
- [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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