Multipliers of elementary operators and comparison of row and column space Schatten p norms

Abstract

Sharp upper estimates for the norm of the weighted elementary operator of the form ∑n = 1∞ Cn Zn An ⊗ Bn Wn Dn, acting from one symmetrically normed ideal of compact Hilbert space operators to another, are given. Particularly, we relate the norm of ∑n = 1∞ Cn Zn An ⊗ An* Wn Cn* with norms of ∑n = 1∞ An ⊗ An* and ∑n = 1∞ Cn ⊗ Cn* on the appropriate domains and co-domains. © 2009 Elsevier Inc. All rights reserved.