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G-narrow operators and G-rich subspaces

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Ivashyna T.

Open Mathematics

2013

tom 11

nr 9

1677-1688

Let X and Y be Banach spaces. An operator G: X → Y is a Daugavet center if ‖G +T‖ = ‖G‖+‖T‖ for every rank-1 operator T. For every Daugavet center G we consider a certain set of operators acting from X, so-called G-narrow operators. We prove that if J is the natural embedding of Y into a Banach space E, then E can be equivalently renormed so that an operator T is (J ○ G)-narrow if and only if T is G-narrow. We study G-rich subspaces of X: Z ⊂ X is called G-rich if the quotient map q: X → X/Z is G-narrow.

Sums of SCD sets and their applications to SCD operators and narrow operators

100%

Kadets V., Shepelska V.

Open Mathematics

2010

tom 8

nr 1

129-134

We answer two open questions concerning the recently introduced notions of slicely countably determined (SCD) sets and SCD operators in Banach spaces. An application to narrow operators in spaces with the Daugavet property is given.

Ograniczanie wyników

2 Open Mathematics

1 Ivashyna T.

1 Kadets V.

1 Shepelska V.

1 2013

1 2010

Wyniki wyszukiwania

G-narrow operators and G-rich subspaces

Sums of SCD sets and their applications to SCD operators and narrow operators