Orlicz-Lorentz Sequence Spaces Equipped with the Orlicz Norm

Kadec–Klee property with respect to the local convergence in measure of Orlicz–Lorentz spaces

“…It is also easy to show that there exists 𝑡 2 > 𝑡 0 such that ∫ and 𝑡 1 is a point of continuity of 𝑥 * . For 𝑢 and 𝑣 defined as above, we have 𝛿 > 0 (see formula (5)). Proceeding analogously as in Case 2, we get a contradiction again.…”

“…At first, studies on their structure concerned the case of the Luxemburg norm (see, e.g., [4, 7, 8, 11–13, 17, 19, 21]). Recently there have been some papers addressing the case of the Orlicz norm (see [10, 23, 24]), but only in articles [5] and [9] it was assumed for the first time that $$\varphi$$ is any Orlicz function and not so‐called $$N$$‐function. In this paper, we continue those studies by finding criteria for the Kadec–Klee property with respect to the local convergence in measure in Orlicz–Lorentz spaces and their subspaces of order continuous elements.…”