Let T be a kernel operator with values in a rearrangement invariant Banach function space X on [0,∞) and defined over simple functions on [0,∞) of bounded support. We identify the optimal domain for T (still with values in X) in terms of interpolation spaces, under appropriate conditions on the kernel and the space X. The techniques used are based on the relation between linear operators and vector measures.
Dato un qualsiasi spazio invariante per riordinamenti su un insieme aperto , si determina il più piccolo spazio invariante per riordinamenti con la proprietà che se è una applicazione che mantiene l'orientamento e , allora appartiene localmente a .
Let be a completely regular Hausdorff space, a boundedly complete vector lattice, the space of all, bounded, real-valued continuous functions on , the algebra generated by the zero-sets of , and a positive linear map. First we give a new proof that extends to a unique, finitely additive measure such that is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of -valued finitely additive measures on are proved, which extend...
Properties of the so called -complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space of all continuous functions, from a zero-dimensional topological space to a non-Archimedean locally convex space , equipped with the topology of uniform convergence on the compact subsets of to be polarly barrelled or polarly quasi-barrelled.
Necessary and sufficient conditions are given so that the space of all continuous functions from a zero-dimensional topological space to a non-Archimedean locally convex space , equipped with the topology of uniform convergence on the compact subsets of , to be polarly absolutely quasi-barrelled, polarly -barrelled, polarly -barrelled or polarly -barrelled. Also, tensor products of spaces of continuous functions as well as tensor products of certain -valued measures are investigated.
We prove that if E is a subset of a Banach space whose density is of measure zero and such that (E, weak) is a paracompact space, then (E, weak) is a Radon space of type (F ) under very general conditions.
We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.
We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.