Characterization of M(H, K)Xin Other (Other) by Dgoodz19
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4.2 Related convergence results 63 (M (Hn , Hn )X M (H, H)X) M (Hn Pn , Hn Pn )(Pn XPn ) M (HP , HP )(P XP ) (2 4L(, ))X .
Therefore, we can repeat the arguments at the end of the part (c) in the proof of Theorem 4.1 to get the desired convergence; in fact, use the above estimate in place of (4.5) and apply Proposition 4.3 (see also Remark 4.2, (1)) together with Pn XPn P XP 0, which is a consequence of the compactness of X. We point out that the arguments in Case (b) in Theorem 4.1 gives us the norm convergence M (Hn , Kn )X M (H,...