PROPERTIES OF OPERATORS WITH SIMILAR REAL AND POSITIVE PARTS

Abstract

Let T = UT

T

be the polar decomposition of T in L(H) where UT is a partial isometry and

= (T∗T)12 satisfying ker(UT) = ker(

) = ker(T). In this thesis, we study the operators which have similar real and positive parts. In other words, we study the properties of operators S and T in L(H) such that

S

and

are similar and Re S and Re T are similar by a single invertible operator X. We provide solution of operators and special relations between such operators S and T. We investigate under what conditions normality is preserved. Also, we study the solution of the operators which have similar imaginary and positive parts. As applications of our results, we provide some examples for them.;이 논문에서는 무한차원 힐버트 공간에서 정의된 유계 선형 작용소 S 와 T의 극 분해를이용하여,두작용소의양의부분

,

와실수부분ReS,ReT 가각각 닮음인 경우 S와 T가 어느 형태로 나타낼 수 있는지, 어떤 성질을 만족하고 어떤 조 건에서 작용소의 정규성 등의 성질들이 보존되는지에 대해 공부한다. 이러한 성질을 갖고있는 S 와 T의 특별한 관계를 찾아보고, 이것을 적용한 예제를 살펴본다.