广义导算子的范数可达性

Norm Attainability of Generalized Derivations

若B(H)表示希尔伯特空间H中所有有界线性算子之集.本文研究了定义在B(H)上的初等算子和广义导算子的范数可达性,证明了如果定义在B(H)中的初等算子和广义导算子是范数可达的,那么这些算子在B(H)中酉群上的限制也是范数可达的.

In this note, the norm attainability of elementary operators and generalized derivations is established. We prove that if an elementary operator and a generalized derivation defined on B（H） are norm-attinable, then the restrictions on the unitary group of B（H） of the elementary operator and the generalized derivation are also norm-attainable, respectively, where B（H） denotes the set of all bounded linear operators on a Hilbert space H.