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Register a new userOn separability of unbounded norm topology
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In this paper, we continue the investigation of topological properties of unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of un-topology in terms of properties of the underlying normed lattice. We apply our results to prove that an order continuous Banach function space $X$ over a semi-finite measure space is separable if and only if it has a $sigma$-finite carrier and is separable with respect to the topology of local convergence in measure. We also address the question when a normed lattice is a normal space with respect to the un-topology.
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In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy--Littlewood constants for $2$-homogeneous polynomials on $ell_p^2$ spaces, $2<pleqinfty$ and lower estimates for polynomials of higher degrees.
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