|
In mathematics, especially operator theory, a hyponormal operator is a generalization of a normal operator. In general, a bounded linear operator ''T'' on a complex Hilbert space ''H'' is said to be ''p''-hyponormal () if: : (That is to say, is a positive operator.) If , then ''T'' is called a hyponormal operator. If , then ''T'' is called a semi-hyponormal operator. Moreoever, ''T'' is said to be log-hyponormal if it is invertible and : An invertible ''p''-hyponormal operator is log-hyponormal. On the other hand, not every log-hyponormal is ''p''-hyponormal. The class of semi-hyponormal operators was introduced by Xia, and the class of p-hyponormal operators was studied by Aluthge, who used what is today called the Aluthge transformation. Every subnormal operator (in particular, a normal operator) is hyponormal, and every hyponormal operator is a paranormal convexoid operator. Not every paranormal operator is, however, hyponormal. == See also == *Putnam’s inequality 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「hyponormal operator」の詳細全文を読む スポンサード リンク
|