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On order structure and operators in L ∞(μ)

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Krasikova I., Martín M., Merí J., Mykhaylyuk V., Popov M.

Open Mathematics

2009

tom 7

nr 4

683-693

It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.

Ograniczanie wyników

1 Open Mathematics

1 Krasikova I.

1 Martín M.

1 Merí J.

1 Mykhaylyuk V.

1 Popov M.

1 2009

Wyniki wyszukiwania

On order structure and operators in L ∞(μ)