On tensor products of operators
Takayuki Furuta, Ritsuo Nakamoto · Proceedings of the Japan Academy Series A Mathematical Sciences · 1969
1o Introduction.In this paper we shall discuss the tensor products of bounded linear operators on a complex Hilbert space H.Following after Halmos [2], we define the numerical radius and the numerical range W(T) as follows: W(T)--((Tx, Definition 1o An operator T is said to be normaloid if IIT]I --r(T), where r(T) means the spectral radius of T, or equivalently Tn II--TII (n-1, 2, ).Definition 2 An operator T is said to be spectraloid if or equivalently Tn IIN --II T 2, ([4]).Definition 3. An operor T is said to be convexoid if W(T)co a(T),