eng
Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2333-1232
2021-10-11
9
2
22
24
10.12691/tjant-9-2-1
TJANT2021921
article
Gaps between Operator Norm and Spectral and Numerical Radii of the Tensor Product of Operators
Zameddin I. Ismailov
ipekpembe@gmail.com
1
Pembe Ipek Al
1
Karadeniz Technical University, Department of Mathematics, 61080, Trabzon, Turkey
One of the fundamental problem of the Spectral Theory of Linear Operators is to determine of the geometric place of the spectrum of the given operator and calculate the spectral and numerical radii of this operator. Other important problem in this theory is to explained the situation the spectral (numerical) radius is equal or not to operator norm. The only known way to calculate the spectral radius to date is the classical Gelfand formula, which often presents great technical challenges. Also, there is not yet a method of calculating the numerical radius for an operator. It should be noted that the finding the numerical range and numerical radius means maximally localizing the spectrum of an operator. The main purpose of this paper is to determine the relations gaps between operator norm and spectral and numerical radii of the tensor product operators associated with the compatible gaps of coordinate operators.
http://pubs.sciepub.com/tjant/9/2/1/tjant-9-2-1.pdf
operator norm
spectral radius
numerical radius