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The almost lattice isometric copies of $c_{0}$ in Banach lattices

Jinxi Chen (2005)

Commentationes Mathematicae Universitatis Carolinae

In this paper it is shown that if a Banach lattice $E$ contains a copy of $c_{0}$ , then it contains an almost lattice isometric copy of $c_{0}$ . The above result is a lattice version of the well-known result of James concerning the almost isometric copies of $c_{0}$ in Banach spaces.

The $b$ -weak compactness of weak Banach-Saks operators

Belmesnaoui Aqzzouz, Othman Aboutafail, Taib Belghiti, Jawad H'michane (2013)

Mathematica Bohemica

We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.

The band generated by homomorphisms on Banach lattices.

David C. Carothers, William A. Feldman (1998)

Extracta Mathematicae

This paper will consider the closure of the set of operators which may be expressed as a sum of lattice homomorphisms whose range is contained in a Dedekind complete Banch lattice.

The boundedness principle for lattice-normed spaces.

Gutman, A.E., Lisovskaya, S.A. (2009)

Sibirskij Matematicheskij Zhurnal

The characteristic of weak convergence on Banach sequence lattices.

Baoxiang Wang, Tingfu Wang (1997)

Collectanea Mathematica

A sufficient and necessary condition for weak convergence of sequences in a class of Banach sequence lattices is obtained. As a direct application, a complete criterion of a weak convergence of sequences in l infinity is formulated.

The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices

D. R. Lewis (1983)

Compositio Mathematica

The Distortion of Hilbert Space.

E. Odell, Th. Schlumprecht (1993)

Geometric and functional analysis

The Hahn-Banach Theorem surveyed [Book]

Gerard Buskes (1993)

The Hahn-Banach-Kantorovich formula for a lattice subdifferential.

Radnaev, V. A. (2002)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

The Hyers-Ulam-Aoki Type Stability of Some Functional Equations on Banach Lattices

Nutefe Kwami Agbeko (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

In Agbeko (2012) the Hyers-Ulam-Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.

The ideal property of tensor products of Banach lattices with applications to the local structure of spaces of absolutely summing operators

N. Nielsen (1982)

Studia Mathematica

The Laplace transform of measures on the cone of a vector lattice.

Egbert Dettweiler (1979)

Mathematica Scandinavica

The lattice copies of $ℓ_{1}$ in Banach lattices

Marek Wójtowicz (2001)

Commentationes Mathematicae Universitatis Carolinae

It is known that a Banach lattice with order continuous norm contains a copy of $ℓ_{1}$ if and only if it contains a lattice copy of $ℓ_{1}$ . The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the $c_{0}$ - and $ℓ_{\infty}$ -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.

The lattice-almost isometric copies of $l^{1}$ and $l^{\infty}$ in Banach lattices.

Chen, Jinxi (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

The lattice-isometric copies of $ℓ_{\infty} (Γ)$ in quotients of Banach lattices.

Wójtowicz, Marek (2003)

International Journal of Mathematics and Mathematical Sciences

The Modulus of a Weakly Compact Operator.

G. Groenewegen, A. van Rooij (1987)

Mathematische Zeitschrift

The order structure of the space of measures with continuous translation

Gérard L. G. Sleijpen (1982)

Annales de l'institut Fourier

Let $G$ be a locally compact group, and let $∥ ∥_{\infty}^{B}$ be a function norm on $L^{1} (G)_{loc}$ such that the space $L^{\infty} (G, B)$ of all locally integrable functions with finite $∥ ∥_{\infty}^{B}$ -norm is an invariant solid Banach function space. Consider the space $L_{RUC} (G, B)$ of all functions in $L^{\infty} (G, B)$ of which the right translation is a continuous map from $G$ into $L^{\infty} (G, B)$ . Characterizations of the case where $L_{RUC} (G, B)$ is a Riesz ideal of $L^{\infty} (G, B)$ are given in terms of the order-continuity of $∥ ∥_{\infty}^{B}$ on certain subspaces of $L^{\infty} (G)$ . Throughout the paper, the discussion is carried out in the context...

The order $σ$ -complete vector lattice of AM-compact operators

Belmesnaoui Aqzzouz, Redouane Nouira (2009)

Czechoslovak Mathematical Journal

We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice $E$ into a Banach lattice $F$ is an order $σ$ -complete vector lattice.

The Projection onto the Center of Operators in a Banach Lattice.

Jürgen Voigt (1988)

Mathematische Zeitschrift

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

Michael Lin (1998)

Studia Mathematica

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