Furuta inequality on operator theory

本文研究算子论中的Furuta不等式。Furuta不等式已被许多学者广泛地推广，本文证明了Furuta不等式在Banach *-代数中也成立，就像在Hilbert空间中一样。其次，我们研究了Hilbert空间上的对数亚正规算子。证明了对数亚正规算子与p = 0的p亚正规算子具有许多相似的性质。例如，Putnam不等式，角切割，Putnam变换。

The purpose of this resarch is to study the Furuta inequality in operator theory. The Furuta inequality has been developped far and wide by many aurthors.In this research, we show that the Furuta inequality holds in Banach *-algebgas as in the case of Hilbert space. Also, we study the Furuta inequality with negative powers and best possibility of the grand Furuta inequality.Next, we study log-hyponormal operators on Hilbert space. We prove that log-hyponormal operators have many similar properties to p-hyponormal operators with p = 0. For examples, Aluthge transform, Putnam's inequality and angular cutting.