Derivations on ideals in commutative AW*-algebras

被引：0

作者：

Chilin V.I. ^{[1
]}

Levitina G.B. ^{[1
]}

机构：

[1] National University of Uzbekistan, Tashkent

来源：

Siberian Advances in Mathematics | 2014年 / 24卷 / 1期

关键词：

boolean algebra; commutative AW*-algebra; derivation; ideal;

D O I：

10.3103/S1055134414010040

中图分类号：

学科分类号：

摘要：

LetA be a commutativeAW*-algebra.We denote by S(A) the *-algebra of measurable operators that are affiliated with A. For an ideal I in A, let s(I) denote the support of I. Let Y be a solid linear subspace in S(A). We find necessary and sufficient conditions for existence of nonzero band preserving derivations from I to Y. We prove that no nonzero band preserving derivation from I to Y exists if either Y ⊂ Aor Y is a quasi-normed solid space. We also show that a nonzero band preserving derivation from I to S(A) exists if and only if the boolean algebra of projections in the AW*-algebra s(I)A is not σ-distributive. © 2014 Allerton Press, Inc.

引用

页码：26 / 42

页数：16

共 16 条

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