关于广义导数的范数

Pure Mathematical Sciences Pub Date : 1900-01-01 DOI:10.12988/pms.2019.9810

Odero Adhiambo Beatrice, J. O. Agure, F. Nyamwala

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引用次数: 0

摘要

设H是无限维复希尔伯特空间，B (H)是H上所有有界线性算子的代数。对于两个有界算子A,B∈B(H)，映射δAB: B(H)→B(H)是由A和B诱导的广义内导数算子，由δAB(X) = AX−XB(1)定义。本文证明了对于所有A,B∈B(H)，广义内导数算子的范数为‖(δAB/B(B(H))‖=‖A‖+‖B‖。数学学科分类:小学47A30，中学47L25

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On the Norm of a Generalized Derivation

Let H be an infinite dimensional complex Hilbert space and B(H) the algebra of all bounded linear operators on H. For two bounded operators A,B ∈ B(H), the map δAB : B(H)→ B(H) is a generalized inner derivation operator induced by A and B defined by δAB(X) = AX −XB (1) In this paper we show that the norm of a generalized inner derivation operator is given by ‖(δAB/B(B(H)))‖ = ‖A‖+‖B‖ for all A,B ∈ B(H). Mathematics Subject Classification: Primary 47A30, Secondary 47L25

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Pure Mathematical Sciences

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