M(r,s)-ideals of compact operators
β Scribed by Haller, Rainis; Johanson, Marje; Oja, Eve
- Book ID
- 118797807
- Publisher
- Springer
- Year
- 2012
- Tongue
- English
- Weight
- 209 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0011-4642
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π SIMILAR VOLUMES
Let r, s g 0, 1 . We prove that a Banach space X satisfies the M r, s -inequality Ε½i.e., 5 5 5 5 5 5 x\*\*\* G r x\*\*\* q s x\*\*\* y x\*\*\* α x\*\*\* g X \*\*\*, . where is the canonical projection of X \*\*\* onto X \* whenever r q sr2 ) 1 and Ε½ . Ε½ . H there exists a norm one projection P on L
Let X = d v p and Y = d w q be Lorentz sequence spaces. We investigate when the space K X Y of compact linear operators acting from X to Y forms or does not form an M-ideal (in the space of bounded linear operators). We show that K X Y fails to be a non-trivial M-ideal whenever p = 1 or p > q. In th