Displaying similar documents to “The lattice-isometric copies of ( Γ ) in quotients of Banach lattices.”

Classification systems and their lattice

Sándor Radeleczki (2002)

Discussiones Mathematicae - General Algebra and Applications


We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent...

Dual Lattice of ℤ-module Lattice

Yuichi Futa, Yasunari Shidama (2017)

Formalized Mathematics


In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic...

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.

Incomparability with respect to the triangular order

Emel Aşıcı, Funda Karaçal (2016)



In this paper, we define the set of incomparable elements with respect to the triangular order for any t-norm on a bounded lattice. By means of the triangular order, an equivalence relation on the class of t-norms on a bounded lattice is defined and this equivalence is deeply investigated. Finally, we discuss some properties of this equivalence.