Abstract
UDC 517.5 In this paper, we give some refinements for the second inequality in where In particular, if is hyponormal by refining the Young inequality with the Kantorovich constant we show that where and . We also give a reverse for the classical numerical radius power inequality for any operator in the case when
Highlights
Suppose that (H, ·, · ) is a complex Hilbert space and B(H) denotes the C∗-algebra of all bounded linear operators on H
It is well known that w(·) defines a norm on B(H), which is equivalent to the usual operator norm ·
An important inequality for w(A) is the power inequality stating that w(An) ≤ wn(A)
Summary
Suppose that (H, ·, · ) is a complex Hilbert space and B(H) denotes the C∗-algebra of all bounded linear operators on H. If A is hyponormal by refining the Young inequality with the Kantorovich constant K(·, ·), we show that w(A) ≤ 2 We give a reverse for the classical numerical radius power inequality w(An) ≤ wn(A) For A ∈ B(H), let w(A) and A denote the numerical radius and the usual operator norm of A, respectively.
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