Acta Mathematica Vietnamica



Some inequalities for continuous functions of selfadjoint operators in Hilbert spaces
S. S. Dragomir



If {Eλ }λR is the spectral family of a bounded selfadjoint operator A on a Hilbert space H and m=minSp(A) and M=maxSp(A), we show that for any continuous function φ: [m,M]C , we have the inequality

φ(A)x,y 2 ( M m0 φ(t) d( m0 t ( E() x,y) ) ) 2 φ(A) x,x φ(A) y,y

for any vectors x and y from H. Some related results and applications are also given.


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