In this paper, we introduce the property (h) on Banach lattices and present its characterization in terms of disjoint sequences. Then, an example is given to show that order-to-norm continuous operator may not be σ-order continuous. Suppose T:E→F order-bounded from Dedekind σ-complete lattice E into complete F. We prove T σ-order-to-norm if only both order weakly compact addition, can represent...

Let E ⊕ F be a direct sum decomposition of a complex Banach lattice X. Garth Dales asked recently whether the equation ‖x+ y‖ = ‖ |x| ∨ |y| ‖ for all x ∈ E and y ∈ F implies that E and F are bands. We show that this is the case by using the theory of hermitian operators. We then show that the same result holds if we replace Dales’s condition by ‖x+ y‖ = ‖(|x|p + |y|p)1/p‖ for any p = 2. To do t...

Using a technique due to Jiménez–Rodríguez, first we prove the complete latticeability of set disjoint non-norm null weakly sequences and regular-polynomially in Banach lattices. Then apply mother vector ? ? ( E ) ? s $\lambda _\pi (E) \setminus \lambda _s(E)$ , which implies ? p ? ? | $(\ell _p\widehat{\otimes }_{|\pi |}E)\setminus (\ell }_{\pi }E)$ where is lattice 1 < ? $1 \infty$ .

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

We consider C -compact orthogonally additive operators in vector lattices. After providing some examples of on a lattice with values Banach space we show that the set those is projection band Dedekind complete all regular operators. In second part article introduce new class lattices, called -complete, and any laterally-to-norm continuous operator from -complete to narrow, which generalizes res...

We show that the solid hull of every weakly precompact set a Banach lattice E is if and only order interval in precompact, or equivalently, disjoint compact precompact. Some results on domination property for positive operators are obtained. Among other things, we that, pair lattices F with $$\sigma $$ -Dedekind complete, operator from to dominated by either norm $$E^{\prime }$$ continuous else