Abstract
Among other results, we have provided general singular value inequality as follows:Let X1,X2,Y1, and Y2 be positive bounded linear operators on a complex separable Hilbert space. Then2sj(X11/2Y11/2−X21/2Y21/2)≤sj(S⊕T) for j=1,2,..., where S=X1+Y1+|X21/2X11/2−Y21/2Y11/2|, and T=X2+Y2+|X11/2X21/2−Y11/2Y21/2|. In particular,sj(X1−X2)≤sj(X1⊕X2) for j=1,2,... Moreover, we have proven several singular value inequalities generalizing the previous inequalities.
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