Abstract
In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.
Highlights
The theory of operator space is a recently arising area in modern analysis, which is a natural non-commutative quantization of Banach space theory
The numerical radius operator space is an important algebraic structure which is introduced by Itoh and Nagisa [17] [18]
Since the relative matrix norms on E are given above, it is evident that these determine numerical radius operator spaces, which we denote by Min E and
Summary
We study some bounded linear maps on the numerical radius operator spaces. If (V , n ) is an operator space and (V , n ) is a numerical radius operator space satisfies v = 1 , the mapping θv : C → V :α → αv is -completely isometric. We consider the condition for finite dimensional numerical radius operator spaces. { } ( f ) = sup ω ( fij (w)) , w∈Ω C0 (Ω) can be seen as a numerical radius operator space. We call such a commutative C*-algebra with a numerical radius norm. Let V be a numerical radius operator space, and let be a commutative C*-algebra with a numerical radius norm.
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