A ug 2 00 7 Multiplication operators on L ( L p ) and l p - strictly singular operators ∗
نویسندگان
چکیده
A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of lp-strictly singular operators, and we also investigate the structure of general lp-strictly singular operators on Lp. The main result is that if an operator T on Lp, 1 < p < 2, is lp-strictly singular and T|X is an isomorphism for some subspace X of Lp, then X embeds into Lr for all r < 2, but X need not be isomorphic to a Hilbert space. It is also shown that if T is convolution by a biased coin on Lp of the Cantor group, 1 ≤ p < 2, and T|X is an isomorphism for some reflexive subspace X of Lp, then X is isomorphic to a Hilbert space. The case p = 1 answers a question asked by Rosenthal in 1976.
منابع مشابه
Multiplication operators on L ( L p ) and ` p - strictly singular operators ∗
A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of `p-strictly singular operators, and we also investigate the structure of general `p-strictly singular operators on Lp. The main result is that if an operator T on Lp, 1 < p < 2, is `p-strictly singular ...
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A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of `p-strictly singular operators, and we also investigate the structure of general `p-strictly singular operators on Lp . The main result is that if an operator T on Lp , 1 < p < 2, is `p-strictly singula...
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