Disjointness Preserving Operators

Automorphisms and Derivations on a Universally Complete Complex f-Algebra

“…The equivalences (1) ↔ (2) ↔ (3) in 3.4 established by A. E. Gutman in [1,16] for the real Kspace B(R) := R↓ contain a solution of A. W. Wickstead's problem of describing the universally complete Kantorovich spaces such that every band preserving linear operator is automatically order bounded [17]. The Boolean valued approach to this topic is set forth in [5].…”

On order bounded disjointness preserving operators

“…Remark. Some aspects of the theory of disjointness preserving operators are presented in [16,18]. The recent results on disjointness preserving operators are surveyed in [9].…”

Boolean-valued introduction to the theory of vector lattices

“…(3) each band preserving endomorphism is a band projection in C ↓; (4) there is no band preserving automorphism other than the identity in C ↓. [16]; he also found an example of a purely nonatomic locally one-dimensional Dedekind complete vector lattice (see [17]). Theorem 5.8 belong to A. G. Kusraev [35].…”

“…A. Abramovich, A. I. Veksler, and A. V. Koldunov [8, Theorem 2.1] and that of P. T. N. McPolin and A. W. Wickstead [48,Theorem 3.2]. Theorem 4,7 was obtained by A. E. Gutman [16]; he also found an example of a purely nonatomic locally one-dimensional Dedekind complete vector lattice (see [17]). Theorem 5.8 belong to A. G. Kusraev [35].…”