Complutense University Library

Estimates of disjoint sequences in Banach lattices and R.I. function spaces

Gonzalo, R. and Jaramillo Aguado, Jesús Ángel (2005) Estimates of disjoint sequences in Banach lattices and R.I. function spaces. Positivity, 9 (2). pp. 233-248. ISSN 1385-1292

[img] PDF
Restricted to Repository staff only until 2020.

147kB

Official URL: http://www.springerlink.com/content/3783587308754353/fulltext.pdf

View download statistics for this eprint

==>>> Export to other formats

Abstract

We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions.

Item Type:Article
Uncontrolled Keywords:Upper and lower estimates; R.I. spaces; smoothness
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16632
References:

Aliprantis, C. and Burkinshaw, O.: Positive Operators, Academic Press, New York,1985.

Bonic, R. and Frampton, J.: Smooth functions on Banach manifolds, J. Math. Mech.15 (1966), 877–898.

Boyd, D. W.: The Hilbert transform on rearrangement invariant spaces, Can. J. Math. 19 (1967), 599–616.

Boyd, D. W.: Indices of function spaces and their relationship to interpolation, Can. J. Math. 21(1969), 1245–1254.

Carothers, N.L.: Rearrangement invariant function subspaces of Lorentz function spaces II, Rocky Mountain J. Math. 17 (1987), 607–616.

Carothers, N.L. and Dilworth, S.T.: Geometry of Lorentz spaces via interpolation, Longhorn Notes Univ. of Texas (1985–86), 107–134.

Castillo, J.M.F., Garc´ia, R. and Gonzalo, R.: Banach spaces in which all multilinear forms are weakly sequentially continuous, Studia Math. 136 (1999), 121–145.

Creekmore, J.: Type and cotype in Lorentz Lp,q-spaces, Indagationes Math. 43 (1981), 141–152.

Deville, R.: Geometrical implications of the existence of very smooth bump functions in Banach spaces, Israel J. Math. 67 (1989), 1–22.

Deville, R., Godefroy, G. and Zizler, V.: Smoothness and Renormings in Banach spaces. Longman, New York, 1993.

Dineen, S.: Complex Analysis on Infinite-dimensional Spaces, Springer, Berlin, 1999.

Fiegel, T., Johnson,W.B. and Tzafriri, L.: On Banach Lattices and Spaces having Local Inconditional Structure, with Applications to Lorentz Function Spaces, J. Approx. Theory 13 (1975), 395–412.

González, M., Gonzalo, R. and Jaramillo, J.A.: Symmetric Polynomials on rearragement invariant function spaces, J. London Math. Soc. 59 (1999), 681–697.

Gonzalo, R.: Upper and lower estimates in Banach sequence spaces, Comment. Math. Univ. Carolinae 36 (1995), 641–653.

Gonzalo, R. and Jaramillo, J.A.: Smoothness and estimates of sequences in Banach spaces, Israel J. Math. 89 (1995) 321–341.

Gonzalo, R. and Jaramillo, J.A.: Compact polynomials between Banach spaces, Proc. Royal Irish Acad. 95A (1995) 213–226.

Gonzalo, R. and Jaramillo, J.A.: High order smoothness in sequence spaces and spreading models, Contemporary Math. 232 (1999), 151–160.

Gonzalo, R. and Maleev, R.P.: Smooth functions in Orlicz function spaces, Arch. Math. 69 (1997), 136–145.

Knaust, H. and Odell, E.: Weakly null sequences with upper lp-estimates, in: Lectures Notes in Math, Springer, Berlin, no. 1470.

Lindenstrauss, J. and Tzafriri, L.: Classical Banach Spaces I, Springer, Berlin, 1977.

Lindenstrauss, J. and Tzafriri, L.: Classical Ranach Spaces II, Springer, Berlin, 1979.

Meshkcov, V. Z.: Smoothness properties in Banach spaces, Stadia Math. 63 (1978) 111–123.

Rabiger, F.: Lower 2-estimates for sequences in Banach lattices, Proc. Am. Math.Soc. 111 (1991), 81–83.

Deposited On:08 Oct 2012 08:13
Last Modified:07 Feb 2014 09:32

Repository Staff Only: item control page