科研之友
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摘要
Let f : [0, infinity) -> [0, infinity) be a concave function and A = @@@ [GRAPHICS] @@@ be a complex partitioned matrix where A(11) and A(22) are square. We show that if A is a normal matrix and the numerical range of A is contained in a sector: @@@ S-alpha = {z is an element of C : Rz > 0, vertical bar Tz vertical bar = Rz tan (alpha)} @@@ for some alpha is an element of [0, pi/2), then parallel to f (vertical bar A vertical bar)parallel to = parallel to f (sec (alpha)vertical bar A(11)|)parallel to + parallel to f (sec (alpha)vertical bar A(22)vertical bar)parallel to @@@ for any unitarily invariant norm parallel to.parallel to. This inequality improves a recent result given by Zhao and Ni.
