Let A be a standard operator algebra acting on a (real or complex) normed space E. For two n-tuples A = (A 1 , . . . , A n ) and B = (B 1 , . . . , B n ) of elements in A, we define the elementary operator R A,B on A by the relation R A,B (X) = n i=1 A i XB i for all X in A. For a single operator A
Isometric properties of elementary operators
โ Scribed by Fernanda Botelho; James Jamison
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 152 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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We establish lower bounds for norms and CB-norms of elementary operators on B(H ). Our main result concerns the operator T a,b x = axb + bxa and we show T a,b a b , proving a conjecture of M. Mathieu. We also establish some other results and formulae for T a,b cb and T a,b for special cases.