Integral expression and comparison of normsin Other (Other) by Dgoodz19
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30 2 Double integral transformations
Proposition . Let (s, t) be the Schur multiplier in the previous lemma. If (s, t) is a Schur multiplier relative to a pair (H, K), then so is the point- wise product (s, t) (s, t)(s, t). Furthermore, for each X B(H) the corresponding double integral transformations (X) and (X) are related by
(X) (HsH )ix ((X))(KsK )ix d1 (x) (HsH )ix ((X))(1 sK ) d2 (x) (1 sH )((X))(KsK )ix d3 (x) ...