On some operator norm inequalities Original Research Article

Let image be the C*-algebra of all bounded linear operators on a complex Hilbert space H, S be an invertible and selfadjoint operator in image and let (I,short parallel.short parallelI) denote a norm ideal of image In this note, we shall show the following inequality:imagefor allXset membership, variantI:short parallelSXS−1−S−1XSshort parallelIless-than-or-equals, slant(short parallelSshort parallelshort parallelS−1short parallel−1)short parallelSXS−1+S−1XSshort parallelI.