p-representable operators in Banach spaces
Let E and F be Banach spaces. An operator T∈L(E,F) is called p-representable if there exists a finite measure μ on the unit ball, B(E*), of E* and a function g∈Lq(μ,F), 1p+1q=1, such thatTx=∫B(E*)〈x,x*〉g(x*)dμ(x*)for all x∈E. The object of this paper is to investigate the class of all p-representabl...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000819 |
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| Summary: | Let E and F be Banach spaces. An operator T∈L(E,F) is called p-representable if there exists a finite measure μ on the unit ball, B(E*), of E* and a function g∈Lq(μ,F), 1p+1q=1, such thatTx=∫B(E*)〈x,x*〉g(x*)dμ(x*)for all x∈E. The object of this paper is to investigate the class of all p-representable operators. In particular, it is shown that p-representable operators form a Banach ideal which is stable under injective tensor product. A characterization via factorization through Lp-spaces is given. |
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| ISSN: | 0161-1712 1687-0425 |