Abstract
A Hilbert space operator T belongs to ∗-class A if . The famous Fuglede-Putnam theorem is as follows: the operator equation implies when A and B are normal operators. In this paper, firstly we prove that if T is a contraction of ∗-class A operators, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator is a strongly stable contraction; secondly, we show that if X is a Hilbert-Schmidt operator, A and are ∗-class A operators such that , then . MSC:47B20, 47A63.
Highlights
Let H be a complex Hilbert space and let C be the set of complex numbers
Firstly we prove that if T is a contraction of ∗-class A operators, either
T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator D = |T | – |T∗| is a strongly stable contraction; secondly, we show that if X is a Hilbert-Schmidt operator, A and (B∗)– are ∗-class A operators such that AX = XB, A∗X = XB∗
Summary
Let H be a complex Hilbert space and let C be the set of complex numbers. Let B(H) denote the C∗-algebra of all bounded linear operators acting on H. Firstly we prove that if T is a contraction of ∗-class A operators, either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator D = |T | – |T∗| is a strongly stable contraction; secondly, we show that if X is a Hilbert-Schmidt operator, A and (B∗)– are ∗-class A operators such that AX = XB, A∗X = XB∗. On ∗-class A contractions Theorem .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
