نتایج جستجو برای: lattice banach space

تعداد نتایج: 588801  

2008
STUART F. CULLENDER COENRAAD C. A. LABUSCHAGNE

We extend Troitsky’s ideas on measure-free martingales on Banach lattices to martingales of operators acting between a Banach lattice and a Banach space. We prove that each norm bounded martingale of cone absolutely summing (c.a.s.) operators (also known as 1-concave operators), from a Banach lattice E to a Banach space Y , can be generated by a single c.a.s. operator. As a consequence, we obta...

1995
FRANCISCO L. HERNANDEZ NIGEL J. KALTON

We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, oo) which is/7-convex for some/? > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if ...

2008
N. J. KALTON Dale Alspach P. WOJTASZCZYK

We are interested in the question when a Banach space X with an unconditional basis is isomorphic (as a Banach space) to an order-continuous nonatomic Banach lattice. We show that this is the case if and only if X is isomorphic as a Banach space with X(i2). This and results of Bourgain are used to show that spaces HI (Tn) are not isomorphic to nonatomic Banach lattices. We also show that tent s...

2014
Wei-Kai Lai

Let φφ be an Orlicz function that has a complementary function φφ∗ and let llφφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev’s Sum Inequality in llφφ⨂� FFXX, the Fremlin projective tensor product of llφφ with a Banach lattice X, and in llφφ⨂� iiXX, the Wittstock injective tensor product of llφφ with a Banach lattice X.

2007
JAN VAN NEERVEN

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces L X , where X is a Banach space and 1 ≤ p < ∞, and extend the result to vector-valued Banach function spaces EX , where E is a Banach function space with order continuous norm. Let X be a Banach space. The problem of describing the compact sets in the Lebesgue-Bochner spaces LpX , ...

2007

1. Let X be a Banach space, and B(X) the Banach algebra of all bounded linear operators in X. The closed two sided ideals of B(X) (actually, of any Banach algebra) form a complete lattice L(X). Aside from very concrete cases, L(X) has not yet been determined; for instance, when X = l, l ^ p < « > , L(X) is a chain (i.e., totally ordered) with three elements: {o}, B(X) and the ideal C(X) of comp...

1994
N. J. Nielsen

We prove that if a non-atomic separable Banach lattice in a weak Hilbert space, then it is lattice isomorphic to L2(0, 1). Introduction This note is to be considered as an addendum to [3], where an extensive study of Banach lattices, which are weak Hilbert spaces, was made. We prove that if a non-atomic separable Banach lattice is a weak Hilbert space then it is lattice isomorphic to L2(0, 1). ...

ژورنال: پژوهش های ریاضی 2022

Suppose E is a Banach lattice. A net  in E is said to be unbounded absolute weak convergent ( uaw-convergent, for short) to  provided that the net  convergences to zero, weakly.  In this note, we further investigate unbounded absolute weak convergence in E. We show that this convergence is stable under passing to and   from ideals and sublattices. Compatible with un-convergenc, we show that ...

2017
M. KANDIĆ

A net (xα) in a Banach lattice X is said to un-converge to a vector x if ∥∥|xα−x|∧u∥∥→ 0 for every u ∈ X+. In this paper, we investigate un-topology, i.e., the topology that corresponds to un-convergence. We show that un-topology agrees with the norm topology iff X has a strong unit. Un-topology is metrizable iff X has a quasi-interior point. Suppose that X is order continuous, then un-topology...

پایان نامه :وزارت علوم، تحقیقات و فناوری - دانشگاه علوم پایه دامغان 1390

the space now known as complete erdos space ec was introduced by paul erdos in 1940 as the closed subspace of the hilbert space ?2 consisting of all vectors such that every coordinate is in the convergent sequence {0} ? { 1 n : n ? n}. in a solution to a problem posed by lex g. oversteegen we present simple and useful topological characterizations of ec. as an application we determine the ...

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