Transactions of the American Mathematical Society, 2014
We study rearrangement invariant spaces with the Daugavet property. The main result of this paper... more We study rearrangement invariant spaces with the Daugavet property. The main result of this paper states that under mild assumptions the only nonseparable rearrangement invariant space X X over an atomless finite measure space with the Daugavet property is L ∞ L_{\infty } endowed with its canonical norm. We also prove that a uniformly monotone rearrangement invariant space over an infinite atomless measure space with the Daugavet property is isometric to L 1 L_1 . As an application we obtain that an Orlicz space over an atomless measure space has the Daugavet property if and only if it is isometrically isomorphic to L 1 L_1 .
Proceedings of the American Mathematical Society, 1995
Criteria for uniform monotonicity, local uniform monotonicity and strict monotonicity of Lorentz ... more Criteria for uniform monotonicity, local uniform monotonicity and strict monotonicity of Lorentz spaces are given.
Abstract. We study M-ideal properties of function and sequence Marcinkiewicz spaces. In particula... more Abstract. We study M-ideal properties of function and sequence Marcinkiewicz spaces. In particular we calculate the duals of the space Σ = L1 +L∞ equipped with two standard norms and investigate when its subspace of order continuous elements is an M-ideal in Σ. A closed subspace Y ...
We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz functio... more We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces $\Lambda_{\varphi,w}$ equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and singular functionals, and we show that the norm of a singular functional is the same regardless of the norm in the space, while the formulas of the norm of general functionals are different for the Luxemburg and Orlicz norm. The relationship between equivalent definitions of the modular $P_{\varphi,w}$ generating the dual space to Orlicz-Lorentz space is discussed in order to compute the norm of a bounded linear functional on $\Lambda_{\varphi,w}$ equipped with Orlicz norm. As a consequence, we show that the order-continuous subspace of Orlicz-Lorentz space equipped with the Luxemburg norm is an $M$-ideal in $\Lambda_{\varphi,w}$, while this is not true for the space with the Orlicz norm when $\varphi$ is an Orlicz $N$-function not satisfying the app...
Transactions of the American Mathematical Society, 2014
We study rearrangement invariant spaces with the Daugavet property. The main result of this paper... more We study rearrangement invariant spaces with the Daugavet property. The main result of this paper states that under mild assumptions the only nonseparable rearrangement invariant space X X over an atomless finite measure space with the Daugavet property is L ∞ L_{\infty } endowed with its canonical norm. We also prove that a uniformly monotone rearrangement invariant space over an infinite atomless measure space with the Daugavet property is isometric to L 1 L_1 . As an application we obtain that an Orlicz space over an atomless measure space has the Daugavet property if and only if it is isometrically isomorphic to L 1 L_1 .
Proceedings of the American Mathematical Society, 1995
Criteria for uniform monotonicity, local uniform monotonicity and strict monotonicity of Lorentz ... more Criteria for uniform monotonicity, local uniform monotonicity and strict monotonicity of Lorentz spaces are given.
Abstract. We study M-ideal properties of function and sequence Marcinkiewicz spaces. In particula... more Abstract. We study M-ideal properties of function and sequence Marcinkiewicz spaces. In particular we calculate the duals of the space Σ = L1 +L∞ equipped with two standard norms and investigate when its subspace of order continuous elements is an M-ideal in Σ. A closed subspace Y ...
We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz functio... more We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces $\Lambda_{\varphi,w}$ equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and singular functionals, and we show that the norm of a singular functional is the same regardless of the norm in the space, while the formulas of the norm of general functionals are different for the Luxemburg and Orlicz norm. The relationship between equivalent definitions of the modular $P_{\varphi,w}$ generating the dual space to Orlicz-Lorentz space is discussed in order to compute the norm of a bounded linear functional on $\Lambda_{\varphi,w}$ equipped with Orlicz norm. As a consequence, we show that the order-continuous subspace of Orlicz-Lorentz space equipped with the Luxemburg norm is an $M$-ideal in $\Lambda_{\varphi,w}$, while this is not true for the space with the Orlicz norm when $\varphi$ is an Orlicz $N$-function not satisfying the app...
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Papers by Anna Kamińska