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

[1]

Albeverio S., Ayupov S.A., Kudaybergenov K.K., Structure of derivations on various algebras of measurable operators for type I von Neumann algebras, J. Funct. Anal., 256, 9, pp. 2917-2943, (2009)

[2]

Ber A.F., Chilin V.I., Sukochev F.A., Non-trivial derivations on commutative regular algebras, Extracta Math., 21, 2, pp. 107-147, (2006)

[3]

Ber A.F., Sukochev F.A., Derivations in the Banach ideals of τ -compact operators

[4]

Ber A.F., Sukochev F.A., Chilin V.I., Derivations in commutative regular algebras, Math. Notes, 75, 3, pp. 418-419, (2004)

[5]

Berberian S.K., Baer *-Rings, (1972)

[6]

Chilin V.I., Partially ordered Baer involutive algebras, J. SovietMath., 37, pp. 1449-1472, (1987)

[7]

Gutman A.E., Kusraev A.G., Kutateladze S.S., The Wickstead problem, Sib. Èlectron. Mat. Izv., 5, pp. 293-333, (2008)

[8]

Kantorovich L.V., Akilov G.P., Functional Analysis, (1982)

[9]

Krein S.G., Petunin Y.I., Semenov E.M., Interpolation of Linear Operators, (1982)

[10]

Kusraev A.G., Vector Duality and Its Applications, (1985)

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