On order structure and operators in L ∞(μ)

• Autorzy: Irina Krasikova , Miguel Martín , Javier Merí , Vladimir Mykhaylyuk , Mikhail Popov
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Narrow operator; The space L ∞; AM-compact operator

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 46B42: Banach lattices

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 683-693

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Irina Krasikova

• Department of Mathematics, Zaporizhzhya National University, Zaporizhzhya, Ukraine

autor

Miguel Martín

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain

autor

Javier Merí

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain

autor

Vladimir Mykhaylyuk

• Department of Mathematics, Chernivtsi National University, Chernivtsi, Ukraine

autor

Mikhail Popov

• Department of Mathematics, Chernivtsi National University, Chernivtsi, Ukraine

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0047-y