The powers of an operator of numerical radius one.
نویسندگان
چکیده
منابع مشابه
Numerical Ranges of the Powers of an Operator
The numerical range W (A) of a bounded linear operator A on a Hilbert space is the collection of complex numbers of the form (Av, v) with v ranging over the unit vectors in the Hilbert space. In terms of the location of W (A), inclusion regions are obtained for W (Ak) for positive integers k, and also for negative integers k if A−1 exists. Related inequalities on the numerical radius w(A) = sup...
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چکیده ندارد.
15 صفحه اولNumerical Radius Norms on Operator Spaces
Abstract. We introduce a numerical radius operator space (X,Wn). The conditions to be a numerical radius operator space are weaker than the Ruan’s axiom for an operator space (X,On). Let w(·) be the numerical radius norm on B(H). It is shown that if X admits a norm Wn(·) on the matrix space Mn(X) which satisfies the conditions, then there is a complete isometry, in the sense of the norms Wn(·) ...
متن کاملOn the Numerical Radius of a Quaternionic Normal Operator
We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternio...
متن کاملFurther inequalities for operator space numerical radius on 2*2 operator matrices
We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. These inequalities contain some upper and lower bounds for operator space numerical radius.
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1971
ISSN: 0026-2285
DOI: 10.1307/mmj/1029000687